Derivatives of Trig Functions (No Chain Rule)

Front

What is the derivative of \( \tan(x) \)?

Back

The derivative of \( \tan(x) \) is \( \sec^2(x) \).

Front

What is the derivative of \( \cot(x) \)?

Back

The derivative of \( \cot(x) \) is \( -\csc^2(x) \).

Front

What is the derivative of \( \sec(x) \)?

Back

The derivative of \( \sec(x) \) is \( \sec(x)\tan(x) \).

Front

What is the derivative of \( \csc(x) \)?

Back

The derivative of \( \csc(x) \) is \( -\csc(x)\cot(x) \).

Front

What is the derivative of \( \sin(x) \)?

Back

The derivative of \( \sin(x) \) is \( \cos(x) \).

Front

What is the derivative of \( \cos(x) \)?

Back

The derivative of \( \cos(x) \) is \( -\sin(x) \).

Front

Find the derivative of \( f(x) = 3x^2 + 5\tan(x) \).

Back

\( f'(x) = 6x + 5\sec^2(x) \).

Front

Find the derivative of \( y = 3x^2 - 4\csc(x) + 2 \).

Back

\( y' = 6x + 4\csc(x)\cot(x) \).

Front

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

Back

\( f'(x) = x^4\cos(x) + 4x^3\sin(x) \).

Front

What is the derivative of \( \sin^2(x) \)?

Back

Using the power rule and chain rule, the derivative is \( 2\sin(x)\cos(x) = \sin(2x) \).