Evaluate the following derivatives. \frac{d}{dx}\int_{3}^{e^{x}}\cos t^{2}dt

tinfoQ 2021-02-13 Answered
Evaluate the following derivatives.
ddx3excost2dt
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Expert Answer

Talisha
Answered 2021-02-15 Author has 93 answers
Step 1
To evaluate the derivative,
ddx3excost2dt
Step 2
According to the Lebnitz Rule of differentiation under the sign of integration,
ddxg(x)h(x)f(t)dt=f(h(x))dh(x)dxf(g(x))dg(x)dx
Step 3
Let us apply the above rule,
3excost2dt=cos(ex)2d(ex)dxcos(3)2d(3)dx
3excost2dt=cose2x(ex)cos9(0)
3excost2dt=excos(e2x)
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