Question

If x=2u²+1 and y=5u³+1, find dy/dx​

Answer 1

Answer:

$\frac{dy}{dx}$ = $\frac{15}{4}$ u

Step-by-step explanation:

$\frac{dy}{dx}$ = $\frac{dy}{du}$ × $\frac{du}{dx}$

differentiate using the power rule

$\frac{d}{dx}$ (a$x^{n}$ ) = na$x^{n-1}$ , and $\frac{d}{dx}$ (constant) = 0

given

x = 2u² + 1

$\frac{dx}{du}$ = 4u , then

$\frac{du}{dx}$ = $\frac{1}{4u}$

y = 5u³ + 1

$\frac{dy}{du}$ = 15u²

then

$\frac{dy}{dx}$ = 15u² × $\frac{1}{4u}$ = $\frac{15}{4}$ u