Find the Derivative - d/dx y=cos(a^7+x^7)

Problem

d()/d(x)*cos(a7+x7)

Solution

1. Identify the outer and inner functions to apply the Chain Rule. The outer function is cos(u) and the inner function is u=a7+x7

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 a7 is 0 and the derivative of x7 is 7*x6

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

d(y)/d(x)=−sin(a7+x7)⋅d()/d(x)*(a7+x7)

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

d(y)/d(x)=−sin(a7+x7)⋅7*x6

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

d(y)/d(x)=−7*x6*sin(a7+x7)

Final Answer

d(cos(a7+x7))/d(x)=−7*x6*sin(a7+x7)

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