Differential Calculus

Derivatives and differentiation

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Expression Derivatives
y = xn dy/dx = nxn-1
y = axn dy/dx = anxn-1
f(x) = axn f'(x) = anxn-1
y = ex dy/dx = ex
y = eax dy/dx = aeax
y = ax dy/dx = ax ln a
y = ln x dy/dx = 1/x
y = sinΘ dy/dΘ = cosΘ
y = cosΘ dy/dΘ = - sinΘ
y = tanΘ dy/dΘ = sec2Θ
y = cotΘ dy/dΘ = cosec2Θ
y = secΘ dy/dΘ = tanΘ secΘ
= sinΘ/cos2Θ
y = cosecΘ
dy/dΘ = - cotΘ cosecΘ
= - cosΘ/sin2Θ
y = sin-1x/a dy/dx = 1/(a2 - x2)1/2
y = cos-1x/a dy/dx = - 1/(a2 - x2)1/2
y = tan-1x/a dy/dx = a/(a2 + x2)
y = cot-1x/a dy/dx = - a/(a2 + x2)
y = sec-1x/a dy/dx = a/(x(x2 - a2)1/2)
y = cosec-1x/a dy/dx = - a/(x(x2 - a2)1/2)

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