Differentiation of Logarithmic and Exponential Functions

Front

What is the derivative of an exponential function of the form y = a^x?

Back

dy/dx = a^x ln(a)

Front

Differentiate the function y = e^(kx) where k is a constant.

Back

dy/dx = k e^(kx)

Front

What is the derivative of a logarithmic function of the form y = log_a(x)?

Back

dy/dx = 1/(x ln(a))

Front

Differentiate the function y = ln(x^k) where k is a constant.

Back

dy/dx = k/x

Front

What is the product rule for differentiation?

Back

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

Front

Differentiate the function y = x^n e^(kx) where n and k are constants.

Back

dy/dx = x^n k e^(kx) + n x^(n-1) e^(kx)

Front

What is the chain rule for differentiation?

Back

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

Front

Differentiate the function y = a^(bx) where a and b are constants.

Back

dy/dx = a^(bx) (b ln(a))

Front

What is the derivative of y = 3^(2x + 5)?

Back

dy/dx = (3^(2x + 5)) (ln(3)) (2)