Evaluate the following derivatives. \frac{d}{dx}\int_{-x}^{x}\frac{dt}{t^{10}+1}

Efan Halliday 2021-02-22 Answered
Evaluate the following derivatives.
ddxxxdtt10+1
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Expert Answer

delilnaT
Answered 2021-02-24 Author has 94 answers
Step 1
g(x)=xxdtt10+1
Let
According to second Fundamental theorem of calculus, for a function,
F(x)=axf(t)dt
which is continuous on [a, x].
F'(x)=f(x)
Step 2
So for function g(x) there exist an antiderivative such that
g(x)=ddxxxdtt10+1
=1x10+1
Thus, the derivative of the function, ddxxxdtt10+1is1x10+1
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