Evaluate
\frac{7}{9}-\frac{77}{9y}
Differentiate w.r.t. y
\frac{77}{9y^{2}}
Graph
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\frac{7\left(y-11\right)}{9y}
Divide \frac{7}{9} by \frac{y}{y-11} by multiplying \frac{7}{9} by the reciprocal of \frac{y}{y-11}.
\frac{7y-77}{9y}
Use the distributive property to multiply 7 by y-11.
\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7\left(y-11\right)}{9y})
Divide \frac{7}{9} by \frac{y}{y-11} by multiplying \frac{7}{9} by the reciprocal of \frac{y}{y-11}.
\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7y-77}{9y})
Use the distributive property to multiply 7 by y-11.
\frac{9y^{1}\frac{\mathrm{d}}{\mathrm{d}y}(7y^{1}-77)-\left(7y^{1}-77\right)\frac{\mathrm{d}}{\mathrm{d}y}(9y^{1})}{\left(9y^{1}\right)^{2}}
For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.
\frac{9y^{1}\times 7y^{1-1}-\left(7y^{1}-77\right)\times 9y^{1-1}}{\left(9y^{1}\right)^{2}}
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}.
\frac{9y^{1}\times 7y^{0}-\left(7y^{1}-77\right)\times 9y^{0}}{\left(9y^{1}\right)^{2}}
Do the arithmetic.
\frac{9y^{1}\times 7y^{0}-\left(7y^{1}\times 9y^{0}-77\times 9y^{0}\right)}{\left(9y^{1}\right)^{2}}
Expand using distributive property.
\frac{9\times 7y^{1}-\left(7\times 9y^{1}-77\times 9y^{0}\right)}{\left(9y^{1}\right)^{2}}
To multiply powers of the same base, add their exponents.
\frac{63y^{1}-\left(63y^{1}-693y^{0}\right)}{\left(9y^{1}\right)^{2}}
Do the arithmetic.
\frac{63y^{1}-63y^{1}-\left(-693y^{0}\right)}{\left(9y^{1}\right)^{2}}
Remove unnecessary parentheses.
\frac{\left(63-63\right)y^{1}+\left(-\left(-693\right)\right)y^{0}}{\left(9y^{1}\right)^{2}}
Combine like terms.
-\frac{-693y^{0}}{\left(9y^{1}\right)^{2}}
Subtract 63 from 63.
-\frac{-693y^{0}}{9^{2}y^{2}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
-\frac{-693y^{0}}{81y^{2}}
Raise 9 to the power 2.
\frac{\left(-\left(-693\right)\right)y^{0}}{81y^{2}}
Multiply 1 times 2.
\left(-\frac{-693}{81}\right)y^{-2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{77}{9}y^{-2}
Do the arithmetic.
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}