Use the Fundamental Theorem of Calculus to find the derivative of the function.

Question

Link to equation: https://ibb.co/k6s3vD9

g'(x) = ?

Answer 1

Hi,

g(x) = ∫₁^x 7/(t³+1) dt

g'(x) = 7/(x³ +1)

in fact you need to know: g(x) = ∫a^u(x) f(t) dt --------> g'(x) = u'(x) * f( u(x) )

I hope it worked for you.

Minoo

Answer 2

Using the FTC, for these kind of problems:

d/dx∫₁^x f(t) dt

just replace the t's with x.

g'(x) =( ∫₁^x 7/(t³+1)dt )'= 7/(x³+1)

Note that if the upper limit of the integral is a function, then you have to use the chain rule too.

d/dx∫₁^h(x) f(t) dt = f(h(x))h'(x)