How do you differentiate f(x) = sin(x²)?

Question

16175 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-22T12:50:52

$(df)/(dx)=2xcos(x^2)$

Let $f(x)=sin(g(x))$ and $g(x)=x^2$

hence $(df)/(dx)=(df)/(dg)xx(dg)/(dx)$

= $cos(g(x))xx2x$

= $2xcos(g(x))$

= $2xcos(x^2)$

Answer 2 · 2018-07-22T13:06:50

$f'(x)=2x\cos(x^2)$

Given function:

$f(x)=\sin(x^2)$

Differentiating above function w.r.t. $x$ using chain rule:

$d/dxf(x)=d/dx\sin(x^2)$

$f'(x)=\cos(x^2)\frac{d}{dx}(x^2)$

$=\cos(x^2)(2x)$

$=2x\cos(x^2)$