What is the derivative of $sin 5 x$ $sin 5x$ ?

Question

5993 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-02T01:58:04

$\frac{d}{d x} sin (5 x) = 5 cos (5 x)$ $d/dxsin(5x)=5cos(5x)$

When applying the Chain Rule to trigonometric functions such as sine,

$\frac{d}{d x} sin (u) = cos u \cdot \frac{d u}{d x}$ $d/dxsin(u)=cosu*(du)/dx$

In this case, $u = 5 x,$ $u=5x,$ and so

$\frac{d}{d x} sin (5 x) = cos (5 x) \cdot \frac{d}{d x} 5 x$ $d/dxsin(5x)=cos(5x)*d/dx5x$

$\frac{d}{d x} sin (5 x) = 5 cos (5 x)$ $d/dxsin(5x)=5cos(5x)$

Answer 2 · 2018-04-02T02:15:17

$5 cos (5 x)$ $5cos(5x)$

We're dealing with a composite function, and whenever we want to differentiate composite functions, we use the Chain Rule stated below:

$f'(g(x))*g'(x)$

Our composite function is $sin(5x)$ , where:

$f(x)=sinx$ and $g(x)=5x$

$f'(x)=cosx$ and $g'(x)=5$

Now we just plug in! We get:

$cos(5x)*5$

Which we can rewrite as

$5cos(5x)$

What is the derivative of sin 5xsin5xsin 5x?