Help please: find the following derivative.

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Expert Answers
gsarora17 eNotes educator| Certified Educator

As per fundamental theorem of calculus,

`F(t)=int_a^bf(t)dt=F(b)-F(a)`

where F(t) is the antiderivative of f(t) and F'(t)=f(t),

`d/dxint_a^bf(t)dt=b'F'(b)-a'F'(a)`

Here a=0 so F(a)=0 , b=x^5 

`F'(x)=d/dxint_0^(x^5)f(x)dx=b'*f(b)`

`F'(x)=5x^4sin((x^5)^5)`

`F'(x)=5x^4sin(x^25)`