Quick Help - Differentiating

[EIRE2003]

What are the rules for differentiating tan, sin & cos?

I know cos = -sin

tan = sin/cos?

[whozum]

Be careful of what you type.

You can derive sin's derivative (say that five times fast) using the limit definition, from there a simple Taylor series expansion will get you the other two, or knowing sinx' = cosx and cosx' = -sinx, you can use the quotient rule to find tanx.

[PhysicsinCalifornia]

Yea, just like what Whozum said...

if f(x) = \sin \theta,f'(x) = \cos \theta
f(x) = \cos \theta, f'(x) = -\sin \theta
f(x) = \tan \theta, f'(x) = \sec^2 \theta
f(x) = \csc \theta, f'(x) = -\csc\theta \cot\theta
f(x) = \sec \theta, f'(x) = \sec\theta \tan\theta
f(x)= \cot\theta, f'(x) = -\csc^2\theta

Try finding the derivative of the inverse trig functions :rolleyes:

[Jameson]

You are correct \frac{d}{dx}\cos{x} = -\sin{x}

,and I assume you know that \frac{d}{dx}\sin{x} = \cos{x}.

Using these two definitions, use the quotient rule to find the derivative of tanx as Whozum said above.

\frac{d}{dx}\frac{u}{v} = \frac{vu' - uv'}{v^2}

Express tangent as \frac{\sin{x}}{\cos{x}} and see what you get using the rule above.

Jameson