The first derivative of a continuous function y = f(x) is y' = x(x - 30)². Find y' and then use the graphing procedure to sketch the general shape of the graph of f. y"=0 Choose the correct graph below.

Q: 27. y = x²(1 - In x²)

A: To find the derivative of the following function.

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: = Vx* – - 4 cos x+/7x %3D

A:

Q: Find the first derivative f' and the original function f. f"(x) = x³ - 12x, ƒ'(1) = 0, ƒ(1) = 10

A: Topic - Differential equations We are given f''(x)=x3-12x ,f'(1)=0 ,f(1)=10 ∫xndx=xn+1n+1+C

Q: Find the derivative of the function h(w) = -7w¯4 +6/w. %3D h'(w) :

A: The function is  h(w) =-7w-4+6w. We know that derivative of wn, i.e., dwndw = nwn-1.

Q: The first derivative of a continuous function y = f(x) is y' = x(x - 9)². Find y' and then use the…

A:

Q: Differentiate the function. 6x²-1 3x³+4 y= y' = 5

A:

Q: If f(x) = x e sinx , find f'(x) . Graph f and  f' on the samescreen and comment.

A: f(x)=xesinxf'(x)=esinx+xesinxcosx