Calculus Jeopardy

FTC

100

This is a function that is the opposite of a derivative.

What is an antiderivative?

200

This function measures accumulation.

What is an integral?

300

This theorem connects these two core concepts of calculus.

What is differentiation and integration?

400

Differentiation and integration are ____ operations.

What are inverse operations?

500

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)?

Product Rule

100

This is the derivative of 6x sin x.

What is 6 sin x + 6x cos x?

200

If h(x)=f(x)g(x), then h'(x)=...?

What is h'(x) = f(x)g'(x) + f'(x)g(x)?

300

This is the derivative of x ln x.

What is ln x + 1?

400

This is the derivative of (9x²+3)(2x⁴).

What is (18x * 2x⁴)+((9x² + 3)8x³)?

500

Find f'(x) when f(x) = (4x² - x)(x³ - 8x² + 12).

What is f'(x) = 20x⁴ - 132x³ + 24x² + 96x - 12?

Chain Rule

100

If h(x) = f(g(x)), h'(x) = ...?

What is f’(g(x))g’(x)?

200

This is the derivative of (x²+3)⁵.

What is 10x(x² + 3)⁴?

300

This is the derivative of sin(4x).

What is 4 cos(4x)?

400

This is the derivative of e^2x.

What is 2e^2x?

500

This is the derivative of (x² + 9)^1/2.

What is x/(x² + 9)^1/2?

Quotient Rule

100

If h(x) = f(x) - g(x), h'(x) = ...?

What is h'(x) = g(x)f'(x) - f(x)g'(x) / g(x)² ?

200

This is the derivative of x²/(x + 1).

What is (x² + 2x)/(x + 1)?

300

This is the derivative of sin x/cos x.

What is sec²x?

400

This is the derivative of e^x/x.

What is e^x(x - 1)/x²?

500

This is an alternative to using the quotient rule.

What is rewriting the denominator with a negative exponent?

Power Rule

100

If f(x) = xⁿ, f'(x) = ...?

What is nx^n-1?

200

This is the derivative of x¹².

What is 12x¹¹?

300

This is the derivative of 6x³.

What is 18x²?

400

This is the derivative of x^-4.

What is -4x^-5?

500

This is the derivative of -9x^2/7.

What is (-18/7)x^-5/7?