Take the derivative of sin ⁡ ( π x ) x 2 .

Question

Take the derivative of   sin  ⁡  (  π  x  )      x          2      .

rynosluv101swv2s · Accepted Answer

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = \sin (π x)$ and $g (x) = x^{2}$ .

$\sin (π x) \frac{d}{d x} [x^{2}] + x^{2} \frac{d}{d x} [\sin (π x)]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$\sin (π x) (2 x) + x^{2} \frac{d}{d x} [\sin (π x)]$

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = \sin (x)$ and $g (x) = π x$ .

$\sin (π x) (2 x) + x^{2} (\cos (π x) \frac{d}{d x} [π x])$

Differentiate.

$2 x \sin (π x) + π x^{2} \cos (π x)$

Take the derivative of sin ⁡<!-- ⁡

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