Calculus - Log Properties & Derivatives of e^x

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.

Front

Find the first derivative of f(x) = x^2 + e^x - cos(x).

Back

f'(x) = 2x + e^x + sin(x).

Front

Find the second derivative of f(x) = x^2 + e^x - cos(x).

Back

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

Front

Find the derivative of y = 5x^2 e^(3x).

Back

y' = 5xe^(3x)(2 + 3x).

Front

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

Back

y' = 8xe^(x^2).

Front

Find the derivative of f(x) = x e^x.

Back

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

Front

What is the product rule in differentiation?

Back

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

Front

What is the chain rule in differentiation?

Back

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

Front

What is the exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * e^(bx), where e is Euler's number.

Front

What is the significance of the number e in calculus?

Back

The number e is the base of natural logarithms and is used in continuous growth or decay models.