Expert answers to "Find the derivatives. (x2+5x)cos⁡(2x)" - Plainmath

Lennie Carroll

Answered question

2021-09-15

Find the derivatives.

(x^{2} + 5 x) \cos (2 x)

Answer & Explanation

Arnold Odonnell

Skilled2021-09-16Added 109 answers

\frac{d}{d x} [(x^{2} + 5 x) \cos (2 x)]

= \cos (2 x) \frac{d}{d x} (x^{2} + 5 x) + (x^{2} + 5 x) \frac{d}{d x} \cos (2 x)

(using product rule of differentiation)

= \cos (2 x) (2 x + 5) + (x^{2} + 5 x) [- 2 \sin 2 x] (\frac{d (\cos 2 x)}{d x} = - \sin 2 x \frac{d (2 x)}{d x} = - 2 \sin 2 x)

(and using

\frac{d (x^{n})}{d x} = n x^{n - 1}

)

= \cos (2 x) (2 x + 5) - 2 (x^{2} + 6 x) (\sin 2 x)

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