Find the Derivative - d/da y=cos(a^3+x^3)

Problem

d()/d(a)*cos(a3+x3)

Solution

1. Identify the independent variable as a and the dependent variable as y treating x as a constant since the derivative is taken with respect to a

2. Apply the chain rule for the cosine function, where the derivative of cos(u) is −sin(u)⋅d(u)/d(a)

3. Differentiate the inner function a3+x3 with respect to a using the power rule.

d(a3+x3)/d(a)=3*a2+0

4. Multiply the derivative of the outer function by the derivative of the inner function.

d(y)/d(a)=−sin(a3+x3)⋅3*a2

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

d(y)/d(a)=−3*a2*sin(a3+x3)

Final Answer

d(cos(a3+x3))/d(a)=−3*a2*sin(a3+x3)

Want more problems? Check here!