Section 5.1 Derivatives of Exponential Functions, y=ex
Derivative of f(x)= ex is f'(x)= ex
Derivative of composite function
f(x)= eu(x) is f'(x) = u'(x) x eu(x)
The Euler’s number is e=2.718
Section 5.2 The Derivative of the General Exponential Function y= bx
y=bx=> lny=xlnb
\(\frac{1}{y}\) \(\frac{dy}{dx}\) = lnb
\(\frac{dy}{dx}\) = y Inb bx * Inb
Derivative of f(x)= bu(x) is f'(x)=u'(x)* bx * Inb
lim(h->0) \(\frac{b^h-1}{h}\) = Inb
Section 5.3 Optimization Problems involving Exponential Functions
Section 5.3 The derivatives of y=sinx and y=cosx
(sinx)’=cosx
(cosx)’=-sinx
Derivatives of composite Functions
(sin u(x))’=cosx*u'(x)
(cos u(x))’=-sinx*u'(x)
Section 5.4 Derivative of y=tanx
Apply Quotient Rule, (tanx)’= sec²x
Derivative of composite Functions
(tan(u(x))= sec²(u(x))*u'(x)
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