Differentiation
Mathematics for Biotechnology 100 Differentiation Questions with Detailed Solutions | Basic to Advanced Practice This practice set contains different types of differentiation questions including first principle, product rule, quotient rule, chain rule, trigonometric functions, logarithmic functions, exponential functions, inverse trigonometric functions, implicit differentiation, parametric differentiation and higher-order derivatives. Part 1: Differentiation from First Principle Q1. Find the derivative of \( f(x)=x^2+3x \) from first principles. View Solution By definition, \[ f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h} \] Now, \[ f(x+h)=(x+h)^2+3(x+h) \] \[ =x^2+2xh+h^2+3x+3h \] Therefore, \[ f(x+h)-f(x)=2xh+h^2+3h \] \[ f'(x) =\lim_{h\to0} \frac{2xh+h^2+3h}{h} \] \[ =\lim_{h\to0}(2x+h+3) \] Answer: \[ \boxed{f'(x)=2x+3} \] Q2. Find the derivative of \( f(x)=x^3 \) from first principles. View Solution \[ f'(x)= \li...