Evaluate
25x^{\frac{2}{3}}+\frac{12}{x^{3}}
Differentiate w.r.t. x
\frac{50}{3\sqrt[3]{x}}-\frac{36}{x^{4}}
Quiz
Differentiation
5 problems similar to:
\frac { d } { d x } [ 15 x ^ { 5 / 3 } - 6 x ^ { - 2 } - 12 ]
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\frac{5}{3}\times 15x^{\frac{5}{3}-1}-2\left(-6\right)x^{-2-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
25x^{\frac{5}{3}-1}-2\left(-6\right)x^{-2-1}
Multiply \frac{5}{3} times 15.
25x^{\frac{2}{3}}-2\left(-6\right)x^{-2-1}
Subtract 1 from \frac{5}{3}.
25x^{\frac{2}{3}}+12x^{-2-1}
Multiply -2 times -6.
25x^{\frac{2}{3}}+12x^{-3}
Subtract 1 from -2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}