The differential coefficient of a^x + x. x is - Vidyadip

MCQ

The differential coefficient of ${a^x} + \log x.\sin x$ is

✓
${a^x}{\log _e}a + {{\sin x} \over x} + \log x.\cos x$
B
${a^x} + {{\sin x} \over x} + \cos x.\log x$
C
${a^x}\log a + {{\cos x} \over x} + \sin x.\log x.$
D
None of these

✓

Answer

Correct option: A.

${a^x}{\log _e}a + {{\sin x} \over x} + \log x.\cos x$

a
(a) Let $y = {a^x} + \log x.\sin x$

Differentiating w.r.t. $x, $ we get

$\frac{{dy}}{{dx}} = {a^x}{\log _e}(a) + \frac{1}{x}\sin x + \log x.\cos x$.

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