Derivatives of Logs and Exponentials

Front

What is the derivative of f(x) = x^2/e^x?

Back

f'(x) = (2xe^x - x^2e^x) / (e^x)^2

Front

Find the derivative of y = 4e^(x^2).

Back

y' = 8xe^(x^2)

Front

What is the derivative of y = log_4(6x + 5)?

Back

y' = 6/((ln4)(6x + 5))

Front

Find the derivative of y = e^(4x^2 - 5x + 6).

Back

y' = (8x - 5)e^(4x^2 - 5x + 6)

Tags

CCSS.HSF-IF.C.8B

Front

What is the derivative of f(x) = xe^x?

Back

f'(x) = e^x + xe^x

Front

Define the derivative of a function.

Back

The derivative of a function measures how the function's output value changes as its input value changes.

Front

What is the chain rule in differentiation?

Back

The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function.

Front

What is the product rule in differentiation?

Back

The product rule states that the derivative of a product of two functions is given by: (u*v)' = u'v + uv', where u and v are functions of x.

Front

What is the quotient rule in differentiation?

Back

The quotient rule states that the derivative of a quotient of two functions is given by: (u/v)' = (u'v - uv')/v^2.

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.