Find the derivative of the given function sin(3x^5)

To find the derivative of the function sin(3x⁵), we will use the chain rule. The chain rule states that the derivative of a composite function f(g(x)) is f'(g(x)) * g'(x).

In our case, let:

• u = 3x⁵
• f(u) = sin(u)

Now, we need to find the derivatives of f(u) and u:

• f'(u) = cos(u)
• u’ = 15x⁴ (using the power rule)

Now, we can apply the chain rule:

Therefore, the derivative of sin(3x⁵) is:

cos(3x5) * 15x4

This simplifies to:

15x4 * cos(3x5)

In conclusion, the derivative of sin(3x⁵) is 15x⁴ * cos(3x⁵).