# How do you differentiate #sin^2(x) * cos^2(x)#?

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate sin^2(x) * cos^2(x), you can use the product rule. The product rule states that if you have two functions, u(x) and v(x), then the derivative of their product, u(x) * v(x), with respect to x is given by the formula:

(u(x) * v(x))' = u'(x) * v(x) + u(x) * v'(x)

Applying this rule to sin^2(x) * cos^2(x), where u(x) = sin^2(x) and v(x) = cos^2(x), the derivatives are:

u'(x) = 2 * sin(x) * cos(x) (by applying the chain rule) v'(x) = -2 * sin(x) * cos(x) (by applying the chain rule)

Now, substituting these derivatives into the product rule formula:

(sin^2(x) * cos^2(x))' = (2 * sin(x) * cos(x) * cos^2(x)) + (sin^2(x) * (-2 * sin(x) * cos(x)))

Simplifying this expression yields the derivative of sin^2(x) * cos^2(x):

(sin^2(x) * cos^2(x))' = 2 * sin(x) * cos^3(x) - 2 * sin^3(x) * cos(x)

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7