Evaluate
n
Differentiate w.r.t. n
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\frac{n^{2}}{n^{1}}
Use the rules of exponents to simplify the expression.
n^{2-1}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
n^{1}
Subtract 1 from 2.
n
For any term t, t^{1}=t.
n^{2}\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n})+\frac{1}{n}\frac{\mathrm{d}}{\mathrm{d}n}(n^{2})
For any two differentiable functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.
n^{2}\left(-1\right)n^{-1-1}+\frac{1}{n}\times 2n^{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}.
n^{2}\left(-1\right)n^{-2}+\frac{1}{n}\times 2n^{1}
Simplify.
-n^{2-2}+2n^{-1+1}
To multiply powers of the same base, add their exponents.
-n^{0}+2n^{0}
Simplify.
-1+2\times 1
For any term t except 0, t^{0}=1.
-1+2
For any term t, t\times 1=t and 1t=t.
\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{1}n^{2-1})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}n}(n^{1})
Do the arithmetic.
n^{1-1}
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}.
n^{0}
Do the arithmetic.
1
For any term t except 0, t^{0}=1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\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.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}