Solve 8x7/2+8x7*6/3*2=

$$\frac { 8 x 7 } { 2 } + \frac { 8 x 7 \times 6 } { 3 \times 2 } =$$

Evaluate

$$12x_{7}$$

Solution Steps

Divide 8x_{7} by 2 to get 4x_{7}.

$$4x_{7}+\frac{8x_{7}\times 6}{3\times 2}$$

Cancel out 2\times 3 in both numerator and denominator.

$$4x_{7}+2\times 4x_{7}$$

Multiply 2 and 4 to get 8.

$$4x_{7}+8x_{7}$$

Combine 4x_{7} and 8x_{7} to get 12x_{7}.

$$12x_{7}$$

Differentiate w.r.t. x_7

$$12$$

Steps Using Definition of a Derivative

Divide 8x_{7} by 2 to get 4x_{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{7}}(4x_{7}+\frac{8x_{7}\times 6}{3\times 2})$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x_{7}}(4x_{7}+2\times 4x_{7})$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x_{7}}(4x_{7}+8x_{7})$$

Combine 4x_{7} and 8x_{7} to get 12x_{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{7}}(12x_{7})$$

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

$$12x_{7}^{1-1}$$

Subtract 1 from 1.

$$12x_{7}^{0}$$

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

$$12\times 1$$

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

$$12$$