Differentiate the following equation:
$x^{4} (5 s i n x - 3 c o s x)$

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Solution

We have,

$= \frac{d}{d x} x^{4} (5 s i n x - 3 c o s x)$

$= 5 \frac{d}{d x} x^{4} 5 s i n x - 3 x^{4} c o s x$

$= 5 \frac{d}{d x} (x^{4} s i n x) - 3 \frac{d}{d x} (x^{4} c o s x)$

$= 5 (s i n x \frac{d}{d x} (x^{4}) + x^{4} \frac{d}{d x} (s i n x)) - 3 (c o s x \frac{d}{d x} (x^{4}) + x^{4} \frac{d}{d x} (c o s x))$ [Apply product rule]

$= 5 (s i n x \times 4 x^{3} + x^{4} \times c o s x) - 3 (c o s x \times 4 x^{3} + x^{4} (- s i n x))$

$= 20 x^{3} \times s i n x + 5 x^{4} c o s x - 12 x^{3} c o s x + 3 x^{4} s i n x$

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