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andidious
How do I derive 3^(x^4)?
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!
\[f(x) = 3^{x ^{4}}\] 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 !