Differentiate w.r.t. f
-\frac{1}{f^{2}}
Evaluate
\frac{1}{f}
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\frac{\mathrm{d}}{\mathrm{d}f}(\frac{1}{f})
Since \frac{16}{f} and \frac{15}{f} have the same denominator, subtract them by subtracting their numerators. Subtract 15 from 16 to get 1.
-f^{-1-1}
The derivative of ax^{n} is nax^{n-1}.
-f^{-2}
Subtract 1 from -1.
\frac{1}{f}
Since \frac{16}{f} and \frac{15}{f} have the same denominator, subtract them by subtracting their numerators. Subtract 15 from 16 to get 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
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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}