Question

find the derivative of f(x)= (e^x+9)/(5(4^sqrt(x^3)-cscx)

Answer 1

\[(e ^{x}+9)\div (5\sqrt[4]{x}-\csc x)\]

Answer 2

\(f(x)\) = \(e^x + 9\)
\(f'(x) = e^x\)
\(g(x) = 5x^{1/4}-cscx\)
\(g'(x) = 5/(4x^{3/4})+csc(x)cot(x)\)

Using f, g, and their derivatives, I'll just plug this into the quotient rule:
\[\frac{ e^{x}(5\sqrt[4]{x}-cscx)-(e^{x}+9)(\frac{ 5 }{ 4x^{3/4} }+\csc(x)\cot(x)) }{ (5\sqrt[4]{x}-cscx)^{2} }\]

And then however much you need to simplify it. No matter how brutal the derivative, just work with it in separate chunks and pieces and then put it all together.

Answer 3

it says not to simplify so would that just be the answer without simplifying? @Concentrationalizing

Answer 4

Yep. Wouldnt need to do anything else.