Type a math problem

AC

log

ln

(

)

7

8

9

τ

π

4

5

6

≤

≥

%

θ

1

2

3

<

>

x

i

0

.

y

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Type a math problem

AC

log

ln

(

)

7

8

9

τ

π

4

5

6

≤

≥

%

θ

1

2

3

<

>

x

i

0

.

y

Evaluate

\frac{3x^{2}-30x+2}{\left(x-5\right)^{2}}

$(x−5)_{2}3x_{2}−30x+2 $

Steps Using Derivative Rule for Quotient

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−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.

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{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-2)-\left(3x^{2}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}(x_{1}−5)dxd (3x_{2}−2)−(3x_{2}−2)dxd (x_{1}−5) $

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^{\left(n-1\right)}.

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{\left(x^{1}-5\right)\times 2\times 3x^{\left(2-1\right)}-\left(3x^{2}-2\right)x^{\left(1-1\right)}}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}(x_{1}−5)×2×3x_{(2−1)}−(3x_{2}−2)x_{(1−1)} $

Do the arithmetic.

Do the arithmetic.

\frac{\left(x^{1}-5\right)\times 6x^{1}-\left(3x^{2}-2\right)x^{0}}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}(x_{1}−5)×6x_{1}−(3x_{2}−2)x_{0} $

Expand using distributive property.

Expand using distributive property.

\frac{x^{1}\times 6x^{1}-5\times 6x^{1}-\left(3x^{2}x^{0}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}x_{1}×6x_{1}−5×6x_{1}−(3x_{2}x_{0}−2x_{0}) $

To multiply powers of the same base, add their exponents.

To multiply powers of the same base, add their exponents.

\frac{6x^{\left(1+1\right)}-5\times 6x^{1}-\left(3x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}6x_{(1+1)}−5×6x_{1}−(3x_{2}−2x_{0}) $

Do the arithmetic.

Do the arithmetic.

\frac{6x^{2}-30x^{1}-\left(3x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}6x_{2}−30x_{1}−(3x_{2}−2x_{0}) $

Remove unnecessary parentheses.

Remove unnecessary parentheses.

\frac{6x^{2}-30x^{1}-3x^{2}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}6x_{2}−30x_{1}−3x_{2}−(−2x_{0}) $

Combine like terms.

Combine like terms.

\frac{\left(6-3\right)x^{2}-30x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}(6−3)x_{2}−30x_{1}−(−2x_{0}) $

Subtract 3 from 6.

Subtract $3$ from $6$.

\frac{3x^{2}-30x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

$(x_{1}−5)_{2}3x_{2}−30x_{1}−(−2x_{0}) $

For any term t, t^{1}=t.

For any term $t$, $t_{1}=t$.

\frac{3x^{2}-30x-\left(-2x^{0}\right)}{\left(x-5\right)^{2}}

$(x−5)_{2}3x_{2}−30x−(−2x_{0}) $

For any term t except 0, t^{0}=1.

For any term $t$ except $0$, $t_{0}=1$.

\frac{3x^{2}-30x-\left(-2\right)}{\left(x-5\right)^{2}}

$(x−5)_{2}3x_{2}−30x−(−2) $

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\frac{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-2)-\left(3x^{2}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\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{\left(x^{1}-5\right)\times 2\times 3x^{\left(2-1\right)}-\left(3x^{2}-2\right)x^{\left(1-1\right)}}{\left(x^{1}-5\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^{\left(n-1\right)}.

\frac{\left(x^{1}-5\right)\times 6x^{1}-\left(3x^{2}-2\right)x^{0}}{\left(x^{1}-5\right)^{2}}

Do the arithmetic.

\frac{x^{1}\times 6x^{1}-5\times 6x^{1}-\left(3x^{2}x^{0}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

Expand using distributive property.

\frac{6x^{\left(1+1\right)}-5\times 6x^{1}-\left(3x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

To multiply powers of the same base, add their exponents.

\frac{6x^{2}-30x^{1}-\left(3x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

Do the arithmetic.

\frac{6x^{2}-30x^{1}-3x^{2}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

Remove unnecessary parentheses.

\frac{\left(6-3\right)x^{2}-30x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

Combine like terms.

\frac{3x^{2}-30x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}

Subtract 3 from 6.

\frac{3x^{2}-30x-\left(-2x^{0}\right)}{\left(x-5\right)^{2}}

For any term t, t^{1}=t.

\frac{3x^{2}-30x-\left(-2\right)}{\left(x-5\right)^{2}}

For any term t except 0, t^{0}=1.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

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]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $

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