⭐ CHAPTER 3 – DIFFERENTIATION
3.1 Definition
Derivative represents rate of change.
f′(x)=limh→0f(x+h)−f(x)hf'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}f′
(x)=h→0limhf(x+h)−f(x)
3.2 Standard Derivatives
Power Rule
ddx(xn)=nxn−1\frac{d}{dx}(x^n) = nx^{n-1}dxd(xn)=nxn−1
Trigonometric
(sinx)′=cosx(\sin x)' = \cos x(sinx)′=cosx (cosx)′=−sinx(\cos x)' = -\sin
x(cosx)′=−sinx
Exponential
(ex)′=ex(e^x)' = e^x(ex)′=ex
Logarithmic
(lnx)′=1x(\ln x)' = \frac{1}{x}(lnx)′=x1
3.3 Rules
Product Rule
(uv)′=u′v+uv′(uv)' = u'v + uv'(uv)′=u′v+uv′
Quotient Rule
(uv)′=vu′−uv′v2\left(\frac{u}{v}\right)' = \frac{v u' - u v'}{v^2}(vu )
′=v2vu′−uv′
3.1 Definition
Derivative represents rate of change.
f′(x)=limh→0f(x+h)−f(x)hf'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}f′
(x)=h→0limhf(x+h)−f(x)
3.2 Standard Derivatives
Power Rule
ddx(xn)=nxn−1\frac{d}{dx}(x^n) = nx^{n-1}dxd(xn)=nxn−1
Trigonometric
(sinx)′=cosx(\sin x)' = \cos x(sinx)′=cosx (cosx)′=−sinx(\cos x)' = -\sin
x(cosx)′=−sinx
Exponential
(ex)′=ex(e^x)' = e^x(ex)′=ex
Logarithmic
(lnx)′=1x(\ln x)' = \frac{1}{x}(lnx)′=x1
3.3 Rules
Product Rule
(uv)′=u′v+uv′(uv)' = u'v + uv'(uv)′=u′v+uv′
Quotient Rule
(uv)′=vu′−uv′v2\left(\frac{u}{v}\right)' = \frac{v u' - u v'}{v^2}(vu )
′=v2vu′−uv′
