We have an answer to "Find the derivatives. y=4−5x2sin⁡2x"

iohanetc

Answered question

2021-05-18

Find the derivatives.

y = \frac{4 - 5 x^{2}}{\sin 2 x}

Bella

Skilled2021-05-19Added 81 answers

The given function is

y = \frac{4 - 5 x^{2}}{\sin 2 x}

Obtain the derivative as follows.

\frac{d y}{d x} = \frac{d}{d x} [\frac{4 - 5 x^{2}}{\sin 2 x}]

= \frac{\sin 2 x \frac{d}{d x} (4 - 5 x^{2}) - (4 - 5 x^{2}) \frac{d}{d x} (\sin 2 x)}{\sin^{2} 2 x}

= \frac{(- 10 x) \sin 2 x - 2 (4 - 5 x^{2}) \cos 2 x}{\sin^{2} 2 x}

Thus,

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

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