Solve (x)/(xxxxx\timesxxxxxxxxxxxxxxx) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ x }{ xxxxx \times xxxxxxxxxxxxxxx }$$

Evaluate

$\frac{1}{x^{19}}$

Solution Steps

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{x}{x^{2}xxxxxxxxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$\frac{x}{x^{3}xxxxxxxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $3$ and $1$ to get $4$.

$$\frac{x}{x^{4}xxxxxxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $4$ and $1$ to get $5$.

$$\frac{x}{x^{5}xxxxxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $5$ and $1$ to get $6$.

$$\frac{x}{x^{6}xxxxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $6$ and $1$ to get $7$.

$$\frac{x}{x^{7}xxxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $7$ and $1$ to get $8$.

$$\frac{x}{x^{8}xxxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $8$ and $1$ to get $9$.

$$\frac{x}{x^{9}xxxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $9$ and $1$ to get $10$.

$$\frac{x}{x^{10}xxxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $10$ and $1$ to get $11$.

$$\frac{x}{x^{11}xxxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $11$ and $1$ to get $12$.

$$\frac{x}{x^{12}xxxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $12$ and $1$ to get $13$.

$$\frac{x}{x^{13}xxxxxxx}$$

To multiply powers of the same base, add their exponents. Add $13$ and $1$ to get $14$.

$$\frac{x}{x^{14}xxxxxx}$$

To multiply powers of the same base, add their exponents. Add $14$ and $1$ to get $15$.

$$\frac{x}{x^{15}xxxxx}$$

To multiply powers of the same base, add their exponents. Add $15$ and $1$ to get $16$.

$$\frac{x}{x^{16}xxxx}$$

To multiply powers of the same base, add their exponents. Add $16$ and $1$ to get $17$.

$$\frac{x}{x^{17}xxx}$$

To multiply powers of the same base, add their exponents. Add $17$ and $1$ to get $18$.

$$\frac{x}{x^{18}xx}$$

To multiply powers of the same base, add their exponents. Add $18$ and $1$ to get $19$.

$$\frac{x}{x^{19}x}$$

To multiply powers of the same base, add their exponents. Add $19$ and $1$ to get $20$.

$$\frac{x}{x^{20}}$$

Rewrite $x^{20}$ as $xx^{19}$. Cancel out $x$ in both numerator and denominator.

$$\frac{1}{x^{19}}$$

Differentiate w.r.t. x

$-\frac{19}{x^{20}}$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{xxxxxxxxxxxxxxxxxxx}x^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{19}}x^{0})$$

For any number $a$ except $0$, $a^{0}=1$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{19}})$$

The derivative of a constant term is $0$.

$$0$$