Expert Answer to "Find the derivatives. y=(4x2−6x)cos⁡(2−5x)" - Plainmath

Mylo O'Moore

Answered question

2021-09-22

Find the derivatives.

y = (4 x^{2} - 6 x) \cos (2 - 5 x)

Answer & Explanation

Arnold Odonnell

Skilled2021-09-23Added 109 answers

Step 1
Given function is:

y = (4 x^{2} - 6 x) \cos (2 - 5 x)

We have to find the derivative of y with respect to x.
Step 2
Then we get,

\frac{d y}{d x} = \frac{d}{d x} [(4 x^{2} - 6 x) \cos (2 - 5 x)]

\frac{d y}{d x} = \frac{d}{d x} (4 x^{2} - 6 x) \times \cos (2 - 5 x) + (4 x^{2} - 6 x) \times \frac{d}{d x} [\cos (2 - 5 x)]

\frac{d y}{d x} = (8 x - 6) \cos (2 - 5 x) + (4 x^{2} - 6 x) \times [5 \sin (2 - 5 x)]

\frac{d y}{d x} = 2 (4 x - 3) \cos (2 - 5 x) + 10 x (2 x - 3) \sin (2 - 5 x)

Hence the answer.

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