Question

Find the derivative of function (attachment)​

Answer 1

Given function :-

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$\tt\longmapsto{\dfrac{sin(x + a)}{cosx}}$

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To find :-

• Derivative of the given function.

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Solution :-

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We have a given function, finding the derivative of the given function.

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We can write it as

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$\: \: \: \: \: \: \: \: \bigstar\bf\: \: \: {\dfrac{d}{dx}\: \dfrac{sin (x + a)}{cosx}}$

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$\rm\implies{\dfrac{cosx\: \dfrac{d}{dx}sin(x + a) - sin(x + a) \dfrac{d}{dx}\: cosx}{(cosx)^2}}$

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$\rm\implies{\dfrac{cosx . cos(x + a) + sin(x + a)\: sinx}{cos^2x}}$

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$\rm\implies{\dfrac{cos[x + a - x]}{cos^2x}}$

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$\rm\implies{\dfrac{cos\: a}{cos^2 x}}$

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$\rm\implies{cos\: a \times \dfrac{1}{cos^2}}$

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$\bf\implies{cos\: a . sec^2x}$

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Hence, the derivative of the given function is cos a . sec²x.