Thread: How do you find the derivative of this function?

f(x)=(x^4+1)^(sinx)

Can somebody show me the steps?

Originally Posted by littleblackdress

f(x)=(x^4+1)^(sinx)

Can somebody show me the steps?

Logarithmic Differentiation

Originally Posted by littleblackdress

f(x)=(x^4+1)^(sinx)

Can somebody show me the steps?

y=(x^4+1)^(sinx)

ln(y)
=ln((x^4+1)^(sinx)
=(sinx)ln(x^4+1)
d/dx(lny)=d/dx((sinx)ln(x^4+1))
(1/y)y'=(sinx)((4x^3)/(x^4+1))+((cosx)ln(x^4+1))

now solve for y' (You already know your y which is y=(x^4+1)^(sinx) )

f '(x)=y '