Updated Review for Flashcard 13 Derivative of Logarithmic &Exponentia

Front

What is the derivative of the function y = 5^(3x + 4)?

Back

y' = 3(ln(5))(5^(3x + 4))

Front

Find the derivative of y = 25ln(x) + 3e^x + 13x^2.

Back

y' = \frac{25}{x} + 3e^x + 26x

Front

What is the derivative of y = log_3(5x + 7)?

Back

y' = \frac{5}{(5x + 7) \cdot ln(3)}

Front

Find the derivative of f(x) = 4xe^x.

Back

f'(x) = 4xe^x + 4e^x

Front

What is the derivative of y = e^(3cos(x))?

Back

y' = -3sin(x)e^(3cos(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 if a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).

Front

What is the product rule in differentiation?

Back

The product rule states that if u and v are functions of x, then the derivative of their product is u'v + uv'.

Front

What is the quotient rule in differentiation?

Back

The quotient rule states that if u and v are functions of x, then the derivative of their quotient is (u'v - uv')/v^2.

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.