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Derivative of One Function w.r.t Another

If y = sinx a...

Question

$I f y = s i n x a n d z = 5, t h e n \frac{d y}{d z}$ = _____

A

cos x

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B

–cosx

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C

5

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D

Does not exist

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Solution

The correct option is D Does not exist
We know that $\frac{d y}{d z} = \frac{\frac{d y}{d x}}{\frac{d z}{d x}} . H e r e \frac{d y}{d x} = c o s x a n d \frac{d z}{d x} = 0$ (since it’s a constant function)
So denominator of $\frac{d y}{d z}$ becomes zero and hence $\frac{d y}{d z}$ does not exist.

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