Question

cosec(5x+1) find d/dx​

Answer 1

Answer:-

$\dfrac{d[cosec(5x+1) ]}{dx} = -5 cosec (5x+1) . \: cot (5x+1)$

Explanation:-

Given

cos(5x+1)

To Find

Derivative of the given expression

Solution

w.k.t,

$\dfrac{d(cosec \:x)}{dx} = - cosec \:x . \: cot x$

$\dfrac{d[cosec(5x+1) ]}{dx} = - cosec (5x+1) . \: cot (5x+1) . 5$

$\dfrac{d[cosec(5x+1) ]}{dx} = -5 cosec (5x+1) . \: cot (5x+1)$

Answer 2

$\underline{ \sf \fcolorbox{red}{pink}{ \huge{Solution :)}}}$

Given ,

The function is y = cosec(5x + 1)

$\sf \fbox{\star } \: \frac{dy}{dx} = \frac{d \{cosec(5x + 1) \}}{dx}$

By using chain rule , we get

$\sf \mapsto \frac{dy}{dx} = - cosec(5x + 1)cot(5x + 1) \times \frac{d(5x + 1)}{dx} \\ \\ \sf \mapsto \frac{dy}{dx} = - cosec(5x + 1)cot(5x + 1) \times 5 + 0 \\ \\ \sf \mapsto \frac{dy}{dx} = - 5 \: cosec(5x + 1)cot(5x + 1)$

Hence , the derivative of given function i.e cosec(5x + 1) is -5cosec(5x + 1)cot(5x + 1)

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