Solve 4*27*x*4*27*4*27/4*27*4*27-1*4*27

$$\frac { 4 \cdot 27 \cdot x \cdot 4 \cdot 27 \times 4 \cdot 27 } { 4 \cdot 27 \times 4 \cdot 27 - 1 \times 4 \cdot 27 }$$

Evaluate

$$\frac{11664x}{107}$$

Solution Steps

Multiply 4 and 27 to get 108.

$$\frac{108x\times 4\times 27\times 4\times 27}{4\times 27\times 4\times 27-1\times 4\times 27}$$

Multiply 108 and 4 to get 432.

$$\frac{432x\times 27\times 4\times 27}{4\times 27\times 4\times 27-1\times 4\times 27}$$

Multiply 432 and 27 to get 11664.

$$\frac{11664x\times 4\times 27}{4\times 27\times 4\times 27-1\times 4\times 27}$$

Multiply 11664 and 4 to get 46656.

$$\frac{46656x\times 27}{4\times 27\times 4\times 27-1\times 4\times 27}$$

Multiply 46656 and 27 to get 1259712.

$$\frac{1259712x}{4\times 27\times 4\times 27-1\times 4\times 27}$$

Multiply 4 and 27 to get 108.

$$\frac{1259712x}{108\times 4\times 27-1\times 4\times 27}$$

Multiply 108 and 4 to get 432.

$$\frac{1259712x}{432\times 27-1\times 4\times 27}$$

Multiply 432 and 27 to get 11664.

$$\frac{1259712x}{11664-1\times 4\times 27}$$

Multiply 1 and 4 to get 4.

$$\frac{1259712x}{11664-4\times 27}$$

Multiply 4 and 27 to get 108.

$$\frac{1259712x}{11664-108}$$

Subtract 108 from 11664 to get 11556.

$$\frac{1259712x}{11556}$$

Divide 1259712x by 11556 to get \frac{11664}{107}x.

$$\frac{11664}{107}x$$

Differentiate w.r.t. x

$$\frac{11664}{107} = 109\frac{1}{107} = 109.00934579439253$$

Steps Using Definition of a Derivative

Multiply 4 and 27 to get 108.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{108x\times 4\times 27\times 4\times 27}{4\times 27\times 4\times 27-1\times 4\times 27})$$

Multiply 108 and 4 to get 432.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{432x\times 27\times 4\times 27}{4\times 27\times 4\times 27-1\times 4\times 27})$$

Multiply 432 and 27 to get 11664.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11664x\times 4\times 27}{4\times 27\times 4\times 27-1\times 4\times 27})$$

Multiply 11664 and 4 to get 46656.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{46656x\times 27}{4\times 27\times 4\times 27-1\times 4\times 27})$$

Multiply 46656 and 27 to get 1259712.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{4\times 27\times 4\times 27-1\times 4\times 27})$$

Multiply 4 and 27 to get 108.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{108\times 4\times 27-1\times 4\times 27})$$

Multiply 108 and 4 to get 432.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{432\times 27-1\times 4\times 27})$$

Multiply 432 and 27 to get 11664.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{11664-1\times 4\times 27})$$

Multiply 1 and 4 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{11664-4\times 27})$$

Multiply 4 and 27 to get 108.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{11664-108})$$

Subtract 108 from 11664 to get 11556.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1259712x}{11556})$$

Divide 1259712x by 11556 to get \frac{11664}{107}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11664}{107}x)$$

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

$$\frac{11664}{107}x^{1-1}$$

Subtract 1 from 1.

$$\frac{11664}{107}x^{0}$$

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

$$\frac{11664}{107}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{11664}{107}$$