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

Question

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

$$\begin{array}{l} \displaystyle \frac{d}{dx}a^{x} = a^{x}\ln a \[12pt] \displaystyle f(x) = \frac{3 \cdot 5^{x}}{\cos(x)} \end{array}$$

Accepted Answer

$$f'(x) = \frac{\left(3 \cdot 5^{x}\ln{5}\right)\left(\cos(x)\right) - \left(3 \cdot 5^{x}\right)\left(-\sin(x)\right)}{\left(\cos(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(3 \cdot 5^{x}\right)\left(-\sin(x)\right) - \left(3 \cdot 5^{x}\ln{5}\right)\left(\cos(x)\right)}{\left(\cos(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(3 \cdot 5^{x}\ln{5}\right)\left(\cos(x)\right) + \left(3 \cdot 5^{x}\right)\left(-\sin(x)\right)}{\left(\cos(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(3 \cdot 5^{x}\ln{5}\right)\left(\cos(x)\right) - \left(3 \cdot 5^{x}\right)\left(-\sin(x)\right)}{\cos(x)}$$