Find the Derivative - d/da y=cos(a^5+x^5)

Problem

d()/d(a)*cos(a5+x5)

Solution

1. Identify the function as a composition of functions where the outer function is cos(u) and the inner function is u=a5+x5

2. Apply the chain rule, which states that d()/d(a)*ƒ*(g(a))=ƒ′*(g(a))⋅g(a)′

3. Differentiate the outer function with respect to its argument, which gives −sin(a5+x5)

4. Differentiate the inner function with respect to a Since x is treated as a constant relative to a the derivative of a5+x5 is 5*a4+0

5. Multiply the results of the outer and inner derivatives together.

6. Simplify the expression by moving the power to the front.

Final Answer

d(cos(a5+x5))/d(a)=−5*a4*sin(a5+x5)

Want more problems? Check here!