# How do you calculate the derivative of #int(cos(t^3)+t)# from #x=4# to #x=sinx#?

The derivative is

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

To calculate the derivative of the integral ∫(cos(t^3) + t) from x = 4 to x = sin(x), you can use the Fundamental Theorem of Calculus and the Chain Rule.

First, find the antiderivative of the integrand with respect to t, which gives us F(t) = ∫(cos(t^3) + t) dt.

Next, evaluate F(sin(x)) - F(4) and differentiate the result with respect to x using the Chain Rule.

The derivative of the integral with respect to x is then d/dx [F(sin(x)) - F(4)].

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