FTC
This is a function that is the opposite of a derivative.
What is an antiderivative?
This is the derivative of 6x sin x.
What is 6 sin x + 6x cos x?
If h(x) = f(g(x)), h'(x) = ...?
What is f’(g(x))g’(x)?
If h(x) = f(x) - g(x), h'(x) = ...?
What is h'(x) = g(x)f'(x) - f(x)g'(x) / g(x)2 ?
If f(x) = xn, f'(x) = ...?
What is nxn-1?
This function measures accumulation.
What is an integral?
If h(x)=f(x)g(x), then h'(x)=...?
What is h'(x) = f(x)g'(x) + f'(x)g(x)?
This is the derivative of (x2+3)5.
What is 10x(x2 + 3)4?
This is the derivative of x2/(x + 1).
What is (x2 + 2x)/(x + 1)?
This is the derivative of x12.
What is 12x11?
This theorem connects these two core concepts of calculus.
What is differentiation and integration?
This is the derivative of x ln x.
What is ln x + 1?
This is the derivative of sin(4x).
What is 4 cos(4x)?
This is the derivative of sin x/cos x.
What is sec2x?
This is the derivative of 6x3.
What is 18x2?
Differentiation and integration are ____ operations.
What are inverse operations?
This is the derivative of (9x2+3)(2x4).
What is (18x * 2x4)+((9x2 + 3)8x3)?
This is the derivative of e2x.
What is 2e2x?
This is the derivative of ex/x.
What is ex(x - 1)/x2?
This is the derivative of x-4.
What is -4x-5?
Given f is continuous on the interval [a,b] and F is any function that satisfies F'(x) = f(x).
What is f(x) = F(b)-F(a)?
Find f'(x) when f(x) = (4x2 - x)(x3 - 8x2 + 12).
What is f'(x) = 20x4 - 132x3 + 24x2 + 96x - 12?
This is the derivative of (x2 + 9)1/2.
This is an alternative to using the quotient rule.
What is rewriting the denominator with a negative exponent?
This is the derivative of -9x2/7.
What is (-18/7)x-5/7?