Let f be the linear function f(xr) = -5x + 7. (a) The rate of change of f is (b) The graph of f is a with slope. and y-intercept

Q: Find the derivative of the function. f(x) = ((x2 + 3)5 + x)2

A: We use the power rule and chain rule.

Q: Find the derivatives of the function x²(xy² y)² = x² - y² )

A:

Q: use the Chain Rule to find the derivative. y = (t2 + 3t + 1)−5/2

A: Given: y=t2+3t+1-52 Let, t2+3t+1=u Then, by using the chain rule dydt can be found out as,…

Q: Find the derivative of the function. 7x y = Va2 + 5 y'(x) =

A:

Q: Find the derivative of the function.

A: Given, y=1x2+53

Q: use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A: y = (x4 − x3 − 1)2/3 derivative formula ddxxn=nxn-1

Q: The degree of the derivative of f(x) = (3–x)'(x – 12)° is

A:

Q: Find the derivative of the function. x2 + 3 y = x² – 3

A: Consider the given function y=x2+3x2-34

Q: Find the derivative of the function.

A: We have to find the derivative of the given function   The given function is

Q: Find the derivative of the function (x-2)2 | y = Vx2 +1' 2.

A: We use derivative of u/v=( v derivative of u - u derivative of v)/v2.

Q: Determine the derivative of a quadratic function of general form y=ax2+bx+c.

A:

Q: 4 f(x) = Vx*+2 %3D x*-2

A:

Q: Use the Chain Rule to find the derivative of the function. y = (2x2 − 3)3 y' =

A: The chain rule to find the derivation is,

Q: Use the Chain Rule to find the derivative of the function. y = (x3 + 5x2)−1 y' =

A: The function is given by,

Q: Use the Chain Rule to find the derivative. y = (x4 - x3 - 1)2/3

A: To find the derivative y = x4 - x3 - 123.

Q: Find the derivative of the function.

A: Given y=2x-73

Q: Find the derivative of the function. y = 2x² +3 x² +1 X y' =

A:

Q: Use the chain rule to find the derivative of f(x)=5e^(3x^9−6x^10) f'(x)=____

A:

Q: The derivative of f(x,y)=x^3+y^2 is 3x^2+3y^2. True or False?

A: The given function f(x, y) = x3+y2 Differentiate with respect to x ∂f∂x=3x2 Differentiate with…

Q: b. f(x) = 3v2x %3D

A:

Q: Use the chain rule to find the derivative of f(x)=3e^−4x^9+3x^3   f'(x)=

A:

Q: Use the chain rule to find the derivative of f(x) = 4e7#10 – 7æ° f'(x) %3D

A:

Q: Find the derivative of the function. g(x) = (2 + (x2 + 1)4)3

A: Consider the provided function, gx=2+x2+143 Find the derivative of the function. Applying the chain…

Q: Find the derivative of the function. G(y) =  (y − 2)4 (y2 + 4y)5 G'(y) =

A: G(y)=(y-2)4(y2+4y)5 G'(y)=4(y-2)3(y2+4y)5+(y-2)4 5(y2+4y)4(2y+4)        =(y-2)3…

Q: Find the derivative of the function. y = x2 √(16 − x2)

A: Given:y=x2 16-x2Product of differentiation  formula:ddxuv=uv'+vu'

Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

A:

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

A:

Q: Use the Chain Rule to find the derivative of the function. y (4x2 - 7)3 %3D

A:

Q: Use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A:

Q: Use the chain rule to find the derivative of f(x) = 2e-72° + 32® f' (x) =

A:

Q: How do you linearize a function ƒ(x, y) of two independent variables at a point (x0, y0)? Why might…

A:

Q: Find the derivative of the function. y = (x2 − 6)3

A:

Q: Find the derivative of y = xArcsinx + V1 – x².

A:

Q: Find the derivative of the function. f(x) =  x3 − 4 x2 + 2

A:

Q: What is the derivative of y = √/x? 1x² X 2 2 1 X X 2 23

A:

Q: Use the chain rule to find the derivative of f(x) = 2e5a* + 9x³ %3D f' (x) =

A: We have to find

Q: What is the output when the input is 4 for a linear function that has a y-intercept of 5 and a rate…

A: Given information: The input of the linear function is 4. The y-intercept of 5 and the rate of…

Q: Find the derivative of the function. y = 1/(x2 + 5)3

A: Solution:- The given function is  y=1(x2+5)3

Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

A:

Q: x = -t4 – 5t – 3 2.

A:

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

A:

Q: y = (x² + 2)(x-3)

A: The objective is to find the derivative.

Q: Find the derivative a) y=(5)/(3x^15) b) f(x)=√x c)f(x)=-8x^2-6x+17

A:

Q: Find the derivative of the function. x3 4) y =-1 %3D X- 1

A:

Q: Use the chain rule to find the derivative of f(x) = 3e10z° +9x* f'(x) %3D

A:

Q: Find the derivative of y= (x+2)x+2

A:

Q: Find the derivative of the function. f(x) = x2 + 5 − 3x−2

A: Known fact: ddxxn=nxn-1ddxf±g=dfdx±dgdxddxk=0   where k is constant

Q: find the derivative of y = (x + 1) (x² + 3).

A: Given          y=(x2+1)x3+3

Q: Find the derivative of the function. F(x) = (xª + 7x² – 3)4

A:

Q: Find the derivative of the function y = (x + 3)°(x + 2)².

A: Consider the given function y=x+35x+22.