(A) Given the function $f(x) = 5 \sin x - 6 \cos x + 7$. To find the derivative $f'(x)$,we use the standard derivative rules: $\frac{d}{dx}(\sin x) =

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(A) Given the function $f(x) = 5 \sin x - 6 \cos x + 7$. To find the derivative $f'(x)$,we use the standard derivative rules: $\frac{d}{dx}(\sin x) = \cos x$ $\frac{d}{dx}(\cos x) = -\sin x$ $\frac{d}{dx}(\text{constant}) = 0$ Applying these rules: $f'(x) = \frac{d}{dx}(5 \sin x) - \frac{d}{dx}(6 \cos x) + \frac{d}{dx}(7)$ $f'(x) = 5 \cos x - 6(-\sin x) + 0$ $f'(x) = 5 \cos x + 6 \sin x$.

Class 12 Mathematics Continuity and Differentiation Derivative at a point, Standard differentiation

Medium

Find the derivative of the function: $f(x) = 5 \sin x - 6 \cos x + 7$.

A
$5 \cos x + 6 \sin x$
B
$5 \cos x - 6 \sin x$
C
$-5 \cos x + 6 \sin x$
D
$-5 \cos x - 6 \sin x$

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Derivative at a point, Standard differentiation

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Find the derivative of the function: $f(x) = 5 \sin x - 6 \cos x + 7$.

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