Find the Derivative - d/dx sin(5x^4)

Problem

d(sin(5*x^4))/d(x)

Solution

1. Identify the outer function as sin(u) and the inner function as u=5*x^4

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

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

4. Differentiate the inner function 5*x^4 with respect to x using the power rule to get 20*x^3

5. Multiply the results together and substitute u=5*x^4 back into the expression.

Final Answer

d(sin(5*x^4))/d(x)=20*x^3*cos(5*x^4)

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