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

Problem

d(tan(x3))/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=x3 The derivative of tan(u) is sec2(u)

4. Differentiate the inner function, x3 using the Power Rule.

d(x3)/d(x)=3*x2

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

sec2(x3)⋅3*x2

Final Answer

d(tan(x3))/d(x)=3*x2*sec2(x3)

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