Derivatives

Front

What is the derivative of sin²(x)?

Back

d/dx (sin²(x)) = 2(sin(x))(cos(x))

Front

What is the second derivative of f(x) = x² + e^x - cos(x)?

Back

f''(x) = 2 + e^x + cos(x)

Front

Find the derivative of f(t) = (t² + 2t)⁵.

Back

f'(t) = 5(t² + 2t)⁴(2t + 2)

Front

What is the value of h'(3) if h(t) is a function and h'(t) = 1?

Back

h'(3) = 1

Front

Set up the derivative of y = (3x⁴ - 7)(5x² + 1).

Back

y' = (3x⁴ - 7)(10x) + (12x³)(5x² + 1)

Front

What is the power rule for derivatives?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the product rule for derivatives?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the chain rule for derivatives?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the derivative of e^x?

Back

d/dx (e^x) = e^x.

Front

What is the derivative of cos(x)?

Back

d/dx (cos(x)) = -sin(x).