Calculate the derivatives of the following functions: (a) f(x)= 3x² + 4x + 6

Q: Find the derivative of the function.

A: Use the formula of product rule to find the derivative that is df(x)×g(x)dx=f'(x)×g(x)+f(x)×g'(x)…

Q: Find derivatives of the functions defined as follows: y = -3e3x2+5

A: Given:y=-3e3x2+5

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

A:

Q: Find the derivative of the given function. 3-2х y = 3+2x

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: calculate the derivative h(x) = π2(x − 1)

A: To calculate the derivative: h(x)=π2(x-1). Solution: h(x)=π2(x-1) On differentiating both sides with…

Q: Find the derivative of the function. f(x) = x3x f'(x) =

A:

Q: Find the derivative of the function. F(x) = /1 – 2x

A: Given, Fx=1-2x

Q: Find the derivative of the function f (x)=x-2r.

A:

Q: Find the derivative of the function .

A: Given: f(x) = x -6x3 To find: The derivative of the given function.

Q: Find the derivative of y=-3/(t-2)4

A:

Q: Find the derivative of y = x2-1/2cosx

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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: Find the derivative of the function. g(x) + g'(x) = + 3.

A:

Q: Find the derivative of y = (x - 1) 2× + 1 at x = 2.

A:

Q: Find the derivative of y = ÷+; x2

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Q: Find the derivative of the function. f (x) = 1/ ( 1+ x 2  )

A:

Q: Find the derivative of y= (x+1)^x+1

A: Find the derivative

Q: Find the derivative of the function y=√x2√x.

A:

Q: Find derivatives of the function defined as follows. y = x2e-2x

A: The derivative of a product of functions can be calculated using the product rule. Product rule of…

Q: Find the derivative of the function. y = 10'-x²

A: Derivative indicates rate of change. Use the chain rule: ddxf(g(x)=f'(g(x))g'(x) Use the formula:…

Q: Find the derivative of f (x) = 1x , x = 0.

A: Given: f(x)=x at x=0

Q: Find the derivative of the function. y = 2e* +x2

A:

Q: Find the derivative of the function y=√4-3x.

A:

Q: Find the derivative of the function and then evaluate at the given point. y 3x2-4x; 1,7)

A: To determine the derivative of given function and then evaluate at the point (-1, 7).

Q: Find the derivatives of the functions y = 2e-x + e3x

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Q: Calculate the derivative of the function y=(2−x3)(13+x2).

A:

Q: Find the derivative of y=x2(x3-1)5

A: The given function is: y=x2x3-15

Q: Find the derivative of y = ( 1+x2 )x

A: using logarithmic differentiation and product rule

Q: Find the derivative of the algebraic function.

A: Given algebraic function fx=3x-1x. Differentiating the given function with respect to x,…

Q: Find the derivative of the function. x3 - 1 f(x) : x² +

A: dvu=udv-vduu2

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

A:

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function y=(4x+1)^5(3x+1)^-4

A: We can find the derivative as below.

Q: Find the derivative of the function y=3√x+8x.

A: Given:y=3x+8x

Q: Find the derivative of the function f (x) = Vx /x – 6.

A:

Q: Find the derivatives of the functions y = x3 - 3(x2 + π2)

A: the given function is: y=x3-3x2+π2 we have to find the derivative of the given function.

Q: Find the derivative of the function y = x2x+1

A: We have to find derivative of the function: y=x2x+1  In this situation we use logarithmic property…

Q: Find the derivative of the function. Y- (2x)4

A: The given function is

Q: Find the derivative of the function. y = x*V25 - x²

A:

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

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Q: Find the derivative of y = x²( - %3D x2+1

A:

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

A:

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) = 3x−1

A:

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

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

Q: Find the derivative of the function f(x) = x6x. %3D

A:

Q: Find the derivative of the function  y=[x2 + (1  -3 x)5]3

A:

Q: Find the derivative of the function. 8x - 1 f(x) f'(x) = %3!

A: Given function is     f(x) =8x-1x         We solve by using u/v rule d/dx(u/v) = {vdu/dx -…

Q: Find the derivative of the function y=4√x3.

A: Given expression:y=4x3 Simplify the above expression, y=4x312y=4x32 Now, differentiate the above…