find d^2y/dx^2 in terms of x and y of y^4=x^5

Question

second derivative

Answer 1

well, first you have that relation y^4=x^5. So you wanna put x in function of y then you have

y^4=x^5 =>y=x^(5/4)

Now you can derivate y in relation to x twice:

first derivative is y'=5/4(x^1/4)

second one is y''=5/(16x^(3/4))

Hope I helped