Vault Of Euclid

Derivative of x to the Power of sec(x)

Logarithmic and exponential functions core

Find the derivative of \( y = x^{\sec x} \).

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What you need first

Logarithmic differentiation
The product rule
The chain rule
Derivative of the natural logarithm
Derivative of the secant function
Exponent rules

What this problem tests

Tests the student's ability to recognize when to use logarithmic differentiation and to correctly apply the product and chain rules.

This is a standard calculus problem testing the application of logarithmic differentiation to functions of the form f(x)^g(x).

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