Write the composite function in the form (g(x)). [Identify the inner function u = g(x) and the outer function y = Ru).] (Use non-identity functions for (u) and g(x)-) y = (5 - x")6 ((u), g(x)) = dy Find the derivative dx dy dx

Q: Find the first derivative of y=x arcsin x + √1-x²

A: y=x arcsinx+1-x2

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: Find the derivative of g(x) = In(sin²(ed/x)).

A:

Q: Find the derivative of g(x) = (cos(8x))3

A:

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: use implicit differentiation using partial derivatives to find: a) t for 2x?+3xy- 3y*= 2 b) for y…

A: Using the product rule of derivative, it can be written that ddx(xy)=xdydx+y .

Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

A:

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

A:

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5x2 + 2) 28)…

A:

Q: Calculate the derivative (implicit derivative): y + 19xy = Cos(7x³ - 5y) |

A: topic - implicit differentiation

Q: Find the derivative. y= In x+3 %3D

A:

Q: 1-x Find the derivative of y = arctan %3D 1+x

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: Given that y=cos6θ+15 Find dydθ Needed formulae: xn'=nxn-1 cos x'=-sin x ax'=a

Q: Find the derivative of y with respect to x 3tan-1x + sin-1x = 4

A:

Q: 3x-4 1. Y= Arctan 4

A:

Q: eリ- + 2y eTy x° +

A:

Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

A:

Q: Find the derivative of y with respect to x. y = sec -1 (3x2 + 1), X>0

A:

Q: Find the derivative of function.

A:

Q: Find the derivative. g(x) = cosh(In(x)) g'(x) = ||

A: To determine the derivative of the function.

Q: Find the derivative of y using implicit differentiation ycos(x) = x2 + y2

A:

Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

A:

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: Find the derivative of the function by using the chain rule. sinx (a) h(x) = tan(x³ sinx) (b) y= %3D…

A: To find the derivative of the given function using the chain rule, which is:…

Q: Find the derivative of y with respect to x. 1, 1+x2 In 1- x3 y

A: If you have function f(x) in the numerator and the function g(x) in the denominator, then the…

Q: g(x)%3Dx sin(2*)

A:

Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

A:

Q: y = 3x sin-(x²) + In(1 + 2x). Find y' using derivative rules

A: The given function is as -y = 3xsin-1(x2) + ln(1+2x)Differentiating on both sides with respect to…

Q: Find the derivative of y with respect to x. y = In (tan -1 (9x5))

A: Given : y=lntan-19x5

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

A:

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Find the derivative. y = In(x²)tan (3x) %3D

A: Given:

Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

A:

Q: Use implicit differentiation to find the derivative in the form dy/dx.

A:

Q: Find the second derivative of the implicitly defined function x2+y2=R2 (canonical equation of a…

A: Given function is Differentiating both sides with respect to x, we get

Q: Find the derivative of the function. y = sin2(x2 + 2) y' = %3D

A:

Q: Find the derivative of y with respect to x. y = 3 sin -1 (5x 3)

A: Given data:     The given expression is: y=3sin-1(5x3).   Assume 5x3=u and differentiate it with…

Q: sinx (a) h(x) = tan(x² sin.x) (b) y= V1+cos.x

A:

Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 x/2

A: We have to find derivative of y with respect to the appropriate variable: y=cosec-1x2 Rewriting the…

Q: the function f(x) = In 5x +3x + 13). 6. Differentiate ° 7. Find the derivative of the function .2 y…

A:

Q: Shows the derivative function of: 2u² + 5u, where u = x² + 3x

A: Given:     To determine: derivative of the given function.

Q: Find the derivative of y = arccos x + x 1-x²

A:

Q: Use implicit differentiation by partial derivative to solve for dx of function 3x2 + 2xy = -4y3. %3D

A:

Q: r(x)= cos (3x)

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: