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

Problem

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

Solution

1. Identify the outer function as cos(u) and the inner function as u=a7+x7

2. Apply the chain rule, which states that d(ƒ(u))/d(x)=ƒ(u)′⋅d(u)/d(x)

3. Differentiate the outer function cos(u) with respect to u to get −sin(u)

4. Differentiate the inner function a7+x7 with respect to x Since a is a constant, d(a7)/d(x)=0 and d(x7)/d(x)=7*x6

5. Multiply the results together to find the derivative.

6. Simplify the expression by rearranging the terms.

Final Answer

d(cos(a7+x7))/d(x)=−7*x6*sin(a7+x7)

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