Math Help - Differentiation

1. Differentiation

Hey guys could you just check if i did this right please?

q: Differentiate using the chain rule

a:
$
y(x) = cos(5x^2+8)
$

$
u = (5x^2+8)
$

$
du/dx = 10x
$

$
dy/du = -sin(u)
$

$
dy/dx = -sin(10x)
$

2. Originally Posted by mxmadman_44
Hey guys could you just check if i did this right please?

q: Differentiate using the chain rule

a:
$
y(x) = cos(5x^2+8)
$

$
u = (5x^2+8)
$

$
du/dx = 10x
$

$
dy/du = -sin(u)
$

$
dy/dx = -sin(10x)
$
$
\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}=[-sin(5x^2+8)][10x]
$

RonL

3. Originally Posted by mxmadman_44
Hey guys could you just check if i did this right please?

q: Differentiate using the chain rule

a:
$
y(x) = cos(5x^2+8)
$

$
u = (5x^2+8)
$

$
du/dx = 10x
$

$
dy/du = -sin(u)
$

$
dy/dx = -sin(10x)
$
Hello,

$
dy/du = -sin(u)$
here you have to re-substitute:
$
dy/dx = -sin(5x^2+8) \cdot (10x)$

thanks guys