Solve (8xxxxxxxxxxx)/(136\times88888) | 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

$$\frac{ 8xxxxxxxxxxx }{ 136 \times 88888 }$$

Evaluate

$\frac{x^{11}}{1511096}$

Solution Steps

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

$$\frac{8x^{2}xxxxxxxxx}{136\times 88888}$$

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

$$\frac{8x^{3}xxxxxxxx}{136\times 88888}$$

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

$$\frac{8x^{4}xxxxxxx}{136\times 88888}$$

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

$$\frac{8x^{5}xxxxxx}{136\times 88888}$$

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

$$\frac{8x^{6}xxxxx}{136\times 88888}$$

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

$$\frac{8x^{7}xxxx}{136\times 88888}$$

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

$$\frac{8x^{8}xxx}{136\times 88888}$$

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

$$\frac{8x^{9}xx}{136\times 88888}$$

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

$$\frac{8x^{10}x}{136\times 88888}$$

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

$$\frac{8x^{11}}{136\times 88888}$$

Cancel out $8$ in both numerator and denominator.

$$\frac{x^{11}}{17\times 88888}$$

Multiply $17$ and $88888$ to get $1511096$.

$$\frac{x^{11}}{1511096}$$

Differentiate w.r.t. x

$\frac{11x^{10}}{1511096}$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{2}xxxxxxxxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{3}xxxxxxxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{4}xxxxxxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{5}xxxxxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{6}xxxxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{7}xxxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{8}xxx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{9}xx}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{10}x}{136\times 88888})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x^{11}}{136\times 88888})$$

Cancel out $8$ in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{11}}{17\times 88888})$$

Multiply $17$ and $88888$ to get $1511096$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{11}}{1511096})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$11\times \frac{1}{1511096}x^{11-1}$$

Multiply $11$ times $\frac{1}{1511096}$.

$$\frac{11}{1511096}x^{11-1}$$

Subtract $1$ from $11$.

$$\frac{11}{1511096}x^{10}$$