Differentiate the following functions.

1. \( \displaystyle f(x)= \sqrt[3]{x^4-x^2+e^2}\)


Solution


2. \( \displaystyle f(x)= e^{\sin{x}-2x^3+4x}\)


Solution


3. \( \displaystyle f(t)=te^{5t}\)


Solution


4. \( \displaystyle f(z)= \tan{(5-3z)}(\sqrt{z}+2z)^9\)


Solution


5. \( \displaystyle f(u)=12^{u+\sec{u}}\)


Solution


6. \( \displaystyle f(x)=\sqrt{\frac{e^x+e^{-x}}{\sec{(\sin{x})}}}\)


Solution


7. \( \displaystyle f(x)=\sin^3(e^{\cos^5 x})\)


Solution