Question

If y = sinx + cosx, then dy/dx at x=0 is​

Answer 1

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Answer 2

SOLUTION

GIVEN

y = sinx + cosx

TO DETERMINE

$\displaystyle \sf{ \frac{dy}{dx} \: \: \: at \: \: x = 0}$

EVALUATION

Here the given function is

y = sinx + cosx

Now Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} = \cos x - \sin x}$

Putting x = 0 we get

$\displaystyle \sf{ \frac{dy}{dx} \bigg |_{x = 0} = \cos 0 - \sin 0}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} \bigg |_{x = 0} = 1 - 0}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} \bigg |_{x = 0} = 1 }$

FINAL ANSWER

Hence the required value = 1

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