Solve (48x)+(72x)+(48x)+(72x)

$$( 48 x ) + ( 72 x ) + ( 48 x ) + ( 72 x )$$

Evaluate

$$240x$$

Solution Steps

Combine 48x and 72x to get 120x.

$$120x+48x+72x$$

Combine 120x and 48x to get 168x.

$$168x+72x$$

Combine 168x and 72x to get 240x.

$$240x$$

Differentiate w.r.t. x

$$240$$

Steps Using Definition of a Derivative

Combine 48x and 72x to get 120x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(120x+48x+72x)$$

Combine 120x and 48x to get 168x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(168x+72x)$$

Combine 168x and 72x to get 240x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(240x)$$

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

$$240x^{1-1}$$

Subtract 1 from 1.

$$240x^{0}$$

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

$$240\times 1$$

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

$$240$$