Find the derivative of the following functions ( it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers ) $x^4(5 \sin x-3 \cos x)$

1 Answer

Let $f(x) = x^4(5 \sin x-3 \cos x)$$By product rule, f'(x) = x^4\large\frac{d}{dx}$$(5 \sin x - 3 \cos x)+(5 \sin x - 3 \cos x)\large\frac{d}{dx}$$(x^4) x^4 \bigg[5 \large\frac{d}{dx}$$\sin x-3 \large\frac{d}{dx}$$\cos x \bigg]+(5 \sin x - 3 \cos x)\large\frac{d}{dx}$$(x^4)$
$x^4 [5 \cos x -3(-\sin x)]+(5 \sin x-3 \cos x)(4x^3)$
$x^3 [5x \cos x+ 3x \sin x+20 \sin x-12 \cos x]$
answered Apr 14, 2014

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