Solve 3x(4*5)8/5=

$$3x(4 \times 5) \frac{ 8 }{ 5 } =$$

Evaluate

$$96x$$

Solution Steps

Multiply 3 and 4 to get 12.

$$12x\times 5\times \frac{8}{5}$$

Multiply 12 and 5 to get 60.

$$60x\times \frac{8}{5}$$

Express 60\times \frac{8}{5} as a single fraction.

$$\frac{60\times 8}{5}x$$

Multiply 60 and 8 to get 480.

$$\frac{480}{5}x$$

Divide 480 by 5 to get 96.

$$96x$$

Differentiate w.r.t. x

$$96$$

Steps Using Definition of a Derivative

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x\times 5\times \frac{8}{5})$$

Multiply 12 and 5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(60x\times \frac{8}{5})$$

Express 60\times \frac{8}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{60\times 8}{5}x)$$

Multiply 60 and 8 to get 480.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{480}{5}x)$$

Divide 480 by 5 to get 96.

$$\frac{\mathrm{d}}{\mathrm{d}x}(96x)$$

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

$$96x^{1-1}$$

Subtract 1 from 1.

$$96x^{0}$$

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

$$96\times 1$$

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

$$96$$