Test on Differentiation Formulae

Write the derivative of following

1. \(\frac{d}{dx}\sin x\)
2. \(\frac{d}{dx}\cos x\)
3. \(\frac{d}{dx}\tan x\)
4. \(\frac{d}{dx}x^{n}\)
5. \(\frac{d}{dx}\sec x\)
6. \(\frac{d}{dx}\cos ec \ x\)

Find the derivative of following:

1. \(\frac{d}{dx}\left( \sec x+\tan x\right)\)
2. \(\frac{d}{dx}\left( \sin x-\cos x\right)\)
3. \(\frac{d}{dx}\left( x^{4}-\frac{1}{x^{2}}\right)\)
4. \(\frac{d}{dx}\left( x^{3}\cdot sinx\right)\)
5. \(\frac{d}{dx}\left( \frac{\sec x}{x^{3}}\right)\)
6. \(\frac{d}{dx}\left( \sec x\cdot \tan x\right)\)

Find \(f’\left( x\right)\) if \(f\left( x\right)\)

1. \(\sin ^{4}x\)
2. \(\sin x^{4}\)
3. \(\tan x^{2}\cdot \sin x^{2}\)
4. \(sinn\cdot \cos x+\tan x\)
5. \(\frac{5x^{5}+x^{4}}{\tan x}\)
6. \(\frac{\tan x}{\sin x\cdot \cos x}\)

\(\ce{H2O}\)