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Working rules of
Differentiation |
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d/dx(u + v) = d/dx(u) + d/dx(v) |
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d/dx(u - v) = d/dx(u) - d/dx(v) |
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d/dx(c * u) = c * d/dx(u) ( c =
constant) |
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d/dx(u * v) = v * d/dx(u) + u * d/dx(v) |
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d/dx(u / v) = (v * d/dx(u) - u * d/dx(v)) / v2 |
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Differentiation formula |
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d/dx (constant) = 0 |
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d/dx(xn) = n*xn-1 |
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d/dx(sin x) = cos x |
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d/dx(cos x) = -sin x |
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d/dx(tan x) = sec2x |
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d/dx(cot x) = - cosec2x |
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d/dx (sec x) = sec x * tan x |
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d/dx (cosec x) = - cosec x * cot x |
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d/dx (ex) = ex |
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d/dx (ax) = ax logea |
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d/dx (logex) = 1/x |
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d/dx (sin-1x) = 1/sqrt(1-x2) |
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d/dx (cos-1x) = - 1/sqrt(1-x2) |
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d/dx (tan-1x) = 1/(1 + x2) |
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d/dx (cot-1x) = -1/(1+ x2) |
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d/dx (sec-1x) = 1/ |x| * sqrt(x2 -1) |
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d/dx (cosec-1x) = -1/ |x| * sqrt(x2 -1) |
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d/dx (sqrt(x2 +/- a2)) = x /sqrt(x2 +/-
a2) |
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d/dx (sqrt(a2 - x2) = -x / sqrt(a2 - x2) |
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d/dx (sqrt(x)) = 1/ 2 * sqrt(x) |