Find the Derivative - d/dx tan(5x^3)

Problem

d(tan(5*x3))/d(x)

Solution

1. Identify the outer and inner functions to apply the chain rule. The outer function is tan(u) and the inner function is u=5*x3

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) with respect to u The derivative of tan(u) is sec2(u)

4. Differentiate the inner function 5*x3 with respect to x using the power rule.

(d(5)*x3)/d(x)=15*x2

5. Combine the results by multiplying the derivative of the outer function by the derivative of the inner function.

sec2(5*x3)⋅15*x2

6. Simplify the expression by moving the algebraic term to the front.

Final Answer

d(tan(5*x3))/d(x)=15*x2*sec2(5*x3)

Want more problems? Check here!