ch 2 Jan derivatives/inverses

Front

Differentiate f(x) = sin(x)

Back

The derivative of f(x) = sin(x) is f'(x) = cos(x).

Front

Rewrite with an exponent: \(\sqrt{x}\)

Back

\(x^{\frac{1}{2}}\)

Front

Differentiate \(\frac{d}{dx}(\tan(x^3))\)

Back

\(3x^2\sec^2(x^3)\)

Front

Does this problem require the chain rule? \(\frac{d}{dx}(\tan(x^4))\)

Back

Yes, it requires the chain rule.

Front

What is a DERIVATIVE?

Back

The slope of the TANGENT line to f(x).

Front

Differentiate f(x) = cos(x)

Back

The derivative of f(x) = cos(x) is f'(x) = -sin(x).

Front

Differentiate f(x) = e^x

Back

The derivative of f(x) = e^x is f'(x) = e^x.

Front

Differentiate f(x) = ln(x)

Back

The derivative of f(x) = ln(x) is f'(x) = \frac{1}{x}.

Front

What is the product rule?

Back

If f(x) = u(x)v(x), then f'(x) = u'(x)v(x) + u(x)v'(x).

Front

What is the quotient rule?

Back

If f(x) = \frac{u(x)}{v(x)}, then f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}.