anonymous 3 years ago How do I derive 3^(x^4)?

1. anonymous

Hi andidious, y=3^(x^4) lny = x^4*ln3 using implicit differentiation, (1/y)*(dy/dx)=4x^3*ln3 after simplifying it, you would get: dy/dx = y*4x^3*ln3 = 3^(x^4)*(4x^3)*ln3 Hope it helps!

2. anonymous

$f(x) = 3^{x ^{4}}$ logarithmic differentiation $\left( \ln f \right)\prime = \frac{ f \prime }{ f }$ $\ln f = \ln ( 3^{x ^{4}}) = x ^{4} . \ln 3$ $\left( \ln f \right) \prime = ( x ^{4} . \ln 3 )\prime = 4.x ^{3}.\ln 3$ $f \prime = f.(\ln f)\prime = 3^{x ^{4}} . 4. x ^{3} .\ln3$ almost the same with implicit differentiation !

3. anonymous

thanks so much guys!