Rate of change of sin x with respect to cos x at x-2 will be

What do you understand by rate of change of sinx with respect to cos x? Isn’t it d(sinx)/d(cosx) i.e., derivative of sinx with respect to cosx = d(sinx)/d(cos ...

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Standard XII

Mathematics

Derivative of One Function w.r.t Another

Rate of chang...

Question

Rate of change of sinx with respect to cosx at $x = \frac{π}{2}$ will be ______
_

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Solution

What do you understand by rate of change of sinx with respect to cos x?
Isn’t it $\frac{d (s i n x)}{d (c o s x)}$
i.e., derivative of sinx with respect to cosx $= \frac{d (s i n x)}{d (c o s x)}$
$= \frac{(\frac{d}{d x} (s i n x))}{(\frac{d}{d x} (c o s x))} = \frac{c o s x}{- s i n x} = - c o t x .$
At $x = \frac{π}{2}, c o t x = 0,$ which is the correct answer.

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Rate of change of sinx with respect to cosx at x=π2will be ___________

What do you understand by rate of change of sinx with respect to cos x? Isn’t it d(sinx)d(cosx) i.e., derivative of sinx with respect to cosx =d(sinx)d(cosx) =(ddx(sinx))(ddx(cosx))=cosx−sinx=−cotx. At x=π2,cotx=0, which is the correct answer.

Rate of change of sinx with respect to cosx at $x = \frac{π}{2}$ will be ______
_