Differentiate $\mathrm{f}(x) = \sin^4 x + \cos^4 x$ with respect to $x$, leaving your answer in

Question

Differentiate $\mathrm{f}(x) = \sin^4 x + \cos^4 x$ with respect to $x$, leaving your answer in the form of $a \sin bx$, where $a$ and $b$ are constants to be determined. Differentiate $\mathrm{g}(x) = \sin^6 x + \cos^6 x$ with respect to $x$, leaving your answer in the form of $a \sin bx$, where $a$ and $b$ are constants to be determined.

Accepted Answer

(i) $\mathrm{f}'(x)=-\sin4x$, $a=-1$, $b=4$ (ii) $\mathrm{g}'(x)=-\dfrac32\sin4x$, $a=-\dfrac32$, $b=4$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

Solution:

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