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Derivatives / Power and Sum/Diff Rules (31 questions)

QuestionAnswer
Differentiate $x^2$ $2x$
Differentiate $x^3$. $3x^2$
Differentiate $x^4$. $4x^3$
Differentiate $x^{10}$ $10 x^9$
Differentiate $x^{15}$ $15 x^{14}$
Differentiate $3x^4$. $12x^3$
Differentiate $\frac{1}{x^2}$. $-2x^{-3}$
Differentiate $\frac{3}{x^4}$. $-12x^{-5}$
Differentiate $\frac{-2}{x^3}$. $\frac{6}{x^{4}}$
Differentiate $1.5x^{-2}$. $-\frac{3}{x^3}$
Differentiate $-2.5x^{-4}$. $\frac{10}{x^5}$
Differentiate $2x$. $2$
Differentiate $-2x$. $-2$
Differentiate $-12x$. $-12$
Differentiate $-12x^2$. $-24x$
Differentiate $6x^4$. $24x^3$
Differentiate $24x$. $24$
Differentiate $\sqrt{x}$. $\frac{1}{2} x^{-\frac{1}{2}}$
Differentiate $4\sqrt{x}$. $2 x^{-\frac{1}{2}}$
Differentiate $4\sqrt[4]{x}$. $ x^{-\frac{3}{4}}$
Differentiate $x^{\frac{4}{3}}$. $\frac{4}{3} x^{\frac{1}{3}}$
Differentiate $x^{\frac{7}{2}}$. $\frac{7}{2} x^{\frac{5}{2}}$
Differentiate $x^{\frac{7}{4}}$. $\frac{7}{4} x^{\frac{3}{4}}$
Differentiate $8x^{\frac{7}{4}}$. $14 x^{\frac{3}{4}}$
Differentiate $\frac{2}{\sqrt{x}}$. $- x^{-\frac{3}{2}}$
Differentiate $x^2 + 6x$. $2x +6$
Differentiate $3x^3 + \sqrt{x}$. $9x^2 + \frac{1}{2} x^{-\frac{1}{2}}$
Differentiate $x^2 + 2x + 3$ $2x + 2$
Differentiate $x^2 - 2x + 3$ $2x - 2$
Differentiate $-6x^4 - 12x + 3$ $-24x^3 - 12$
Differentiate $x^4 - \frac{1}{x^2}$ $4x^3 + \frac{2}{x^3}$