Derivative Rules - Multi Chain General Exponential Trigonometric (with Rule) to Derivative

Question

Find the derivative f'(x) using the chain, general exponential, and trigonometric rules.

$$\begin{array}{l} \displaystyle \text{if } y = f(g(x)),\ y' = f'(g(x))\cdot g'(x) \[12pt] \displaystyle f(x) = (2 \cdot 3^{x} + 3\cos(x))^{3} \end{array}$$

Accepted Answer

$$f'(x) = 3(2 \cdot 3^{x} + 3\cos(x))^{2} \cdot \left(2 \cdot 3^{x}\ln{3} - 3\sin(x)\right)$$

Answer

$$f'(x) = 3(2 \cdot 3^{x} + 3\cos(x))^{3} \cdot \left(2 \cdot 3^{x}\ln{3} - 3\sin(x)\right)$$

Answer

$$f'(x) = 3(2 \cdot 3^{x} + 3\cos(x))^{2}$$

Answer

$$f'(x) = (2 \cdot 3^{x} + 3\cos(x))^{2} \cdot \left(2 \cdot 3^{x}\ln{3} - 3\sin(x)\right)$$

Derivative Rules - Multi Chain General Exponential Trigonometric (with Rule) to Derivative

Practice:

Derivative Rules - Multi Chain General Exponential Trigonometric (with Rule) to Derivative