"Find the derivatives of the following sin⁡(ax+b)cos⁡(cx+d)" solved and explained - Plainmath

jernplate8

Answered question

2021-10-11

Find the derivatives of the following

\frac{\sin (a x + b)}{\cos (c x + d)}

Answer & Explanation

Asma Vang

Skilled2021-10-12Added 93 answers

Step 1
Given

\frac{\sin (a x + b)}{\cos (c x + d)}

Step 2 differentiating wrt x
Let

y = \frac{\sin (a x + b)}{\cos (c x + d)}

Differentiating w.r.t x

\frac{d y}{d x} = \frac{\cos (c x + d) \frac{d}{d x} \sin (a x + b) - \sin (a x + b) \frac{d}{d x} \cos (c x + d)}{{| \cos (c x + d) |}^{2}}

= \frac{\cos (c x + d) \cdot \cos (a x + b) a - \sin (a x + b) (- \sin (c x + d) \cdot c)}{\cos^{2} (c x + d)}

= \frac{a \cos (a x + b) \cos (c x + d) + c \sin (a x + b) \sin (c x + d)}{\cos^{2} (c x + d)}

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