Solve 3x/5*7*18

$$\frac { 3 x } { 5 \times 7 \times 18 }$$

Evaluate

$$\frac{x}{210}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{x}{5\times 6\times 7}$$

Multiply 5 and 6 to get 30.

$$\frac{x}{30\times 7}$$

Multiply 30 and 7 to get 210.

$$\frac{x}{210}$$

Differentiate w.r.t. x

$$\frac{1}{210} = 0.004761904761904762$$

Steps Using Definition of a Derivative

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5\times 6\times 7})$$

Multiply 5 and 6 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{30\times 7})$$

Multiply 30 and 7 to get 210.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{210})$$

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

$$\frac{1}{210}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{210}x^{0}$$

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

$$\frac{1}{210}\times 1$$

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

$$\frac{1}{210}$$