Find the Derivative - d/dx tan(x^3)

Problem

d(tan(x^3))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule, which states that the derivative of ƒ*(g(x)) is ƒ^′*(g(x))⋅g(x)^′

3. Differentiate the outer function, tan(u) where u=x^3 The derivative of tan(u) is sec^2(u)

4. Differentiate the inner function, x^3 using the Power Rule.

d(x^3)/d(x)=3*x^2

5. Multiply the results together to find the final derivative.

sec^2(x^3)⋅3*x^2

Final Answer

d(tan(x^3))/d(x)=3*x^2*sec^2(x^3)

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