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1) D' {x n } = nx n-1 2) D'{sin x} = cos x 3) D'{cos x} = -sin x 4) D'{tan x} = sec 2 x 5) D'{sec x} = sec x * tan x 6) D'{cot x} = - cosec 2 x 7) D'{cosec x} = -cosec x * cot x 8) D'{log a x} = 1 log a x x 9) D'{log x} = 1 x 10) D'{a x } = a x log a 11) D'{e x }..

Derivatives of polynomial functions: `d/dx` (c) = 0 `d/dx` (x) = 1 `d/dx ` (cx) = c `d/dx` (x n ) = nx n-1 `d/dx` (cx n ) = ncx n-1 Derivatives of trigonometric functions: `d/dx` (sin x) = cos x `d/dx` (cos x) = - sin x `d/dx ` (tan x) = sec 2 x `d/dx` (cot x) = - cosec 2 x `d/dx` (sec x) = sec x tan x ..

D' {x n } = nx n-1 D'{cos x} = -sin x D'{sin x} = cos x D'{tan x} = sec 2 x D'{sec x} = sec x * tan x D'{cot x} = - cosec 2 x D'{log a x} = `1/x` log a x D'{cosec x} = -cosec x * cot x D'{log x} = `1/x` D'{a x } = a x log a D'{e x } = e x D'{sin- 1 x} = `(1)/(sqrt(1-x^2)) ` ..

1 . ` d / dx` (x n ) = n x n-1 2. `d/dx` (ln x) = `1/x` 3 . `d/dx ` (cos x) = sin x 4. ` d/dx` (e x ) = e x 5. `d/dx` (tan x) = sec 2 x 6 . `d/dx` (sin x) = cos x 7. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 8. . `d/dx` `(u/v)` = `(v(du)/(dx) - u(dv)/(dx))/ v^2` 9. ` d/dx` `(u..

Learn differentiation formulas: 1 . ` d / dx` (x n ) = n x n-1 2. `d/dx` (ln x) = `1/x` 3 . `d/dx ` (cos x) = sin x 4. ` d/dx` (e x ) = e x 5. `d/dx` (tan x) = sec 2 x 6 . `d/dx` (sin x) = cos x 7. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 8. . `d/dx` `(u/v)` ..

1 . ` d / dx` (x n ) = n x n-1 2. `d/dx` (ln x) = `1/x` 3 . `d/dx ` (cos x) = sin x 4. ` d/dx` (e x ) = e x 5. `d/dx` (tan x) = sec 2 x 6 . `d/dx` (sin x) = cos x 7. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 8. . `d/dx` `(u/v)` = `(v(du)/(dx) - u(dv)/(dx))/ v^2` 9. ` d/dx` `(..

`d/dx ` tanx = sec 2 x `d/dx` cotx = csc 2 x `d/dx ` secx = secx tanx `d/dx` cscx = cscx cotx `d/dx` e ax = ae x `d/dx ` a x = ln(a) a x , a>0 & a1 `d/dx` c=0 C - Constant `d/dx` c f(x)=c d/dx f(x) `d/dx` x n = nx n1 `d/dx` sinax = acosax `d/dx` cosax = asinax ..

`d/dx` (c) = 0 `d/dx` (x) = 1 `d/dx ` (cx) = c `d/dx` (x n ) = nx n-1 `d/dx` (cx n ) = ncx n-1 `d/dx` (u + v) = `(du)/dx` + ` (dv)/dx` `d/dx` (u - v) = `(du)/dx` - `(dv)/dx` `d/dx` (uv) = u `(dv)/dx` + v `(du)/dx` `d/dx` (u/v) = (v `(du)/dx` - u `(dv)/dx` )/v 2 `d/dx` (sin x) = cos x `d..

d/dx c=0 C - Constant d/dx c f(x)=c d/dx f(x) d/dx x n = nx n1 d/dx sinax = acosax d/dx cosax = asinax d/dx tanx = sec 2 x d/dx cotx = csc 2 x d/dx secx = secx tanx d/dx cscx = cscx cotx d/dx e ax = ae x d/dx a x = ln(a) a x , a>0 & a1 ..

If f (x) and g(x) are differentiable functions (the derivative exists), c and n are any real numbers, ..

Learn differentiation formulas: 1. `d/dx` (x n ) = n x n-1 2 . `d/dx` (cot x) = cosec 2 x 3. ` d/dx` (sec x) = sec x.tan x 4. `d/dx` (ln x) = `1/x` 5. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 6. `d/dx ` `(sin^(- 1)x)` = ` 1/sqrt(1-x^2)` 7. `d/dx ` `(cos^(- 1)x)` = `- 1..

Learn differentiation formulas: 1. `d/dx` (x n ) = n x n-1 2 . `d/dx` (cot x) = cosec 2 x 3. ` d/dx` (sec x) = sec x.tan x 4. `d/dx` (ln x) = `1/x` 5. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 6. `d/dx ` `(sin^(- 1)x)` = ` 1/sqrt(1-x^2)` 7. `d/dx ` `(cos^(- 1)x)` = `- ..

Learn differentiation formulas: 1. `d/dx` (x n ) = n x n-1 2 . `d/dx` (cot x) = cosec 2 x 3. ` d/dx` (sec x) = sec x.tan x 4. `d/dx` (ln x) = `1/x` 5. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 6. `d/dx ` `(sin^(- 1)x)` = ` 1/sqrt(1-x^2)` 7. `d/dx ` `(cos^(- 1)x)` = `- ..

Learning differentiation formulas: 1. `d/dx` (x n ) = n x n-1 2 . `d/dx` (cot x) = cosec 2 x 3. ` d/dx` (sec x) = sec x.tan x 4. `d/dx` (ln x) = `1/x` 5. `d/dx` (log b u) = `1/(u ln b)` `(du)/(dx)` 6. ` d/dx` `(uv)` = `u(dv)/(dx)` + `v(du)/(dx)` 7 . `d/dx` `(u/v)` = `(v(du)/..

Hints to solve porblems based on differentiation: We first view the problem then see what formula we have to use. Plug in the value of n in the formula for `x^n` then we simplify . Que 1:Find the second derivative of the following function: f(x) = x 3 - 4x 2 + 4x Sol :To find the 1 st derivativ..