How do you apply the product rule repeatedly to find the derivative of f(x) = (x^4 +x)*e^x*tan(x)f(x)=(x4+x)⋅ex⋅tan(x) ?
1 Answer
Aug 10, 2014
f'(x)=e^x((4x^3+1)tan(x)+(x^4+x)tan(x)+(x^4+x)sec^2x) Solution
f(x)=(x^4+x)⋅e^x⋅tan(x) For problems, having more than two functions, like
f(x)=u(x)*v(x)*w(x) then, differentiating both sides with respect to
x using Product Rule, we get
f'(x)=u'(x)*v(x)*w(x)+u(x)*v'(x)*w(x)+u(x)*v(x)*w'(x) similarly, following the same pattern for the given problem and differentiating with respect to
x ,
f'(x)=(4x^3+1)⋅e^x⋅tan(x)+(x^4+x)⋅e^x⋅tan(x)+(x^4+x)⋅e^x⋅sec^2x simplifying further,
f'(x)=e^x*((4x^3+1)⋅tan(x)+(x^4+x)⋅tan(x)+(x^4+x)⋅sec^2x)
