Question

Find dy/dx as a function of x when y = sin⁵(x)

Answer 1

To find dy/dx, we can apply the chain rule.

Let's differentiate y = sin⁵(x) term by term:

dy/dx = d/dx (sin⁵(x))

Using the chain rule, we have:

dy/dx = 5(sin⁴(x)) * d/dx(sin(x))

To find d/dx(sin(x)), we can differentiate sin(x) with respect to x:

d/dx(sin(x)) = cos(x)

Now, substituting this back into the equation:

dy/dx = 5(sin⁴(x)) * cos(x)

Therefore, dy/dx as a function of x is:

dy/dx = 5sin⁴(x) * cos(x)