Find out the answer to "Evaluate the following derivatives. ddx∫x5sin⁡w6dw" - Plainmath

Clifland

Answered question

2021-02-14

Evaluate the following derivatives.

\frac{d}{d x} \int_{x}^{5} {\sin w}^{6} d w

Answer & Explanation

Theodore Schwartz

Skilled2021-02-16Added 99 answers

Step 1
We first switch the limits by changing the sign

\frac{d}{d x} \int_{x}^{5} {\sin w}^{6} d w

= \frac{d}{d x} [- \int_{5}^{x} {\sin w}^{6} d w]

= - \frac{d}{d x} [\int_{5}^{x} {\sin w}^{6} d w]

Step 2
Then we use the second fundamental theorem of calculus to find the derivative

= - \frac{d}{d x} [\int_{5}^{x} {\sin w}^{6} d w]

= - \sin (x^{6})

Answer:

- \sin (x^{6})

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