Question

I need help answering question 4, I’m not sure I how to solve it

Answer 1

I usually skip the calculus but here goes

$\sin y = 5x^4 - 5$

Taking derivatives with respect to x,

$\dfrac{ d (\sin y)}{dx} = \dfrac{ d(5x^4 - 5)}{dx}$

$\cos y \dfrac {dy}{dx} = 20 x^3$

$\dfrac {dy}{dx} = \dfrac{ 20 x^3}{\cos y}$

At $(x,y)=(1,\pi)$ we get

$\dfrac {dy}{dx} = \dfrac{ 20 (1)^3}{\cos \pi} = -20$

Answer: -20