Exercise · ZW-BASIC-DIFFERENTIATION-RULES-004 · ★★☆ Intermediate
Differentiate \(f(x)=3 \sqrt{x} + \frac{1}{x^{2}}\).
Choose one option.
Show answer
- C. \(- \frac{2}{x^{3}} + \frac{3}{2 \sqrt{x}}\)
Explanation
Differentiate term by term with \((c\,x^{n})'=c\,n\,x^{n-1}\); the derivative of a constant is 0. The result is \(- \frac{2}{x^{3}} + \frac{3}{2 \sqrt{x}}\).
Review the concept: Basic differentiation rules
The derivative of a constant is \(0\) and that of \(x^n\) is \(n\,x^{n-1}\). The derivative is also linear: the derivative of a sum is the sum of the derivatives and constants factor out.
\[\begin{gathered}\frac{d}{dx}x^{n}=nx^{n-1}\\ (cf+g)'=cf'+g'\end{gathered}\]
More practice problems: basic differentiation rules
- ZW-BASIC-DIFFERENTIATION-RULES-001 Differentiate f(x)=5 x^4 - 3 x^2 + 7 x - 2.
- ZW-BASIC-DIFFERENTIATION-RULES-002 Differentiate f(x)=4 x^3 + 2 x - 9.
- ZW-BASIC-DIFFERENTIATION-RULES-003 Differentiate f(x)=x^5 - 3 x^2 + 7.
- ZW-BASIC-DIFFERENTIATION-RULES-005 Differentiate f(x)=x^6.
- ZW-BASIC-DIFFERENTIATION-RULES-006 Differentiate f(x)=(7)/(x^3).
- ZW-BASIC-DIFFERENTIATION-RULES-007 Differentiate g(t)=π^2+6 t^2.
- ZW-BASIC-DIFFERENTIATION-RULES-008 Differentiate h(x)=√[3]x^2+(4)/(x).
- ZW-BASIC-DIFFERENTIATION-RULES-009 Differentiate f(x)=-8.
← ZW-BASIC-DIFFERENTIATION-RULES-003 ZW-BASIC-DIFFERENTIATION-RULES-005 →