# Problem of the Week

## Updated at Jul 2, 2018 5:37 PM

How would you differentiate $$\ln{x}\sec{x}$$?

Below is the solution.

$\frac{d}{dx} \ln{x}\sec{x}$

 1 Use Product Rule to find the derivative of $$\ln{x}\sec{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} \ln{x})\sec{x}+\ln{x}(\frac{d}{dx} \sec{x})$2 The derivative of $$\ln{x}$$ is $$\frac{1}{x}$$.$\frac{\sec{x}}{x}+\ln{x}(\frac{d}{dx} \sec{x})$3 Use Trigonometric Differentiation: the derivative of $$\sec{x}$$ is $$\sec{x}\tan{x}$$.$\frac{\sec{x}}{x}+\ln{x}\sec{x}\tan{x}$Donesec(x)/x+ln(x)*sec(x)*tan(x)