Solve 54x-12x-12x-15x

$$54 x - 12 x - 12 x - 15 x$$

Evaluate

$$15x$$

Solution Steps

Combine 54x and -12x to get 42x.

$$42x-12x-15x$$

Combine 42x and -12x to get 30x.

$$30x-15x$$

Combine 30x and -15x to get 15x.

$$15x$$

Differentiate w.r.t. x

$$15$$

Steps Using Definition of a Derivative

Combine 54x and -12x to get 42x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(42x-12x-15x)$$

Combine 42x and -12x to get 30x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x-15x)$$

Combine 30x and -15x to get 15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x)$$

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

$$15x^{1-1}$$

Subtract 1 from 1.

$$15x^{0}$$

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

$$15\times 1$$

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

$$15$$