Find the Derivative - d/dx y=cos(a^6+x^6)

Problem

d()/d(x)*cos(a6+x6)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is cos(u) and the inner function is u=a6+x6

2. Differentiate the outer function with respect to u The derivative of cos(u) is −sin(u)

3. Differentiate the inner function with respect to x Since a is a constant, the derivative of a6 is 0 and the derivative of x6 is 6*x5

4. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function.

d(cos(a6+x6))/d(x)=−sin(a6+x6)⋅d(a6+x6)/d(x)

5. Substitute the derivative of the inner function into the expression.

d(cos(a6+x6))/d(x)=−sin(a6+x6)⋅6*x5

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

Final Answer

d(cos(a6+x6))/d(x)=−6*x5*sin(a6+x6)

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