Question

Calculate the derivative ddx∫e^(10x)x⁸ln(t)dt using part 2 of the fundamental theorem of calculus.

A) e^(10x)(x⁸)
B) e^(10x)(8x⁷)
C) e^(10x)(8x⁸)
D) e^(10x)(9x⁸)

Answer 1

To calculate the derivative of the given integral expression, we apply part 2 of the fundamental theorem of calculus. The derivative is e^(10x) * 80x⁷ln(t).

Step-by-step explanation:

To calculate the derivative of the given expression, d/dx∫e^(10x)x⁸ln(t)dt, we can use part 2 of the fundamental theorem of calculus. This theorem states that the derivative of the integral of a function with respect to a variable is equal to the integrand evaluated at the upper limit of integration, multiplied by the derivative of the upper limit.

In this case, the upper limit of integration is x, so we need to take the derivative of e^(10x)x⁸ln(t) with respect to x.

The derivative of e^(10x) with respect to x is e^(10x) * 10, and the derivative of x⁸ln(t) with respect to x is 8x⁷ln(t). Multiplying these two derivatives together, we get e^(10x) * 10 * 8x⁷ln(t) = e^(10x) * 80x⁷ln(t).