Question

Find the derivative of: (see picture)

Answer 1

Find f'(x) when

Answer 2

i got -(x/(2+3x^2)) but its not right

Answer 3

this is a cleaver question, but the derivative of an integral is the function it's self. the derivative undoes the integral

Answer 4

but the answer should be in terms of x

Answer 5

Using the fundamental theorem of calculus to find the derivative (with respect to x) of an integral like


seems to cause students great difficulty. We'll try to clear up the confusion.

Here's the fundamental theorem of calculus:

Theorem If f is a function that is continuous on an open interval I, if a is any point in the interval I, and if the function F is defined by

then the derivative of F(x) is F'(x) = f(x) for every x in the interval I.

(Sometimes this theorem is called the second fundamental theorem of calculus.)

Another way of stating the conclusion of the fundamental theorem of calculus is: