Solve 24^3x-32^2x+8x-1

$${ 24 }^{ 3 } x- { 32 }^{ 2 } x+8x-1$$

Evaluate

$$12808x-1$$

Solution Steps

Calculate 24 to the power of 3 and get 13824.

$$13824x-32^{2}x+8x-1$$

Calculate 32 to the power of 2 and get 1024.

$$13824x-1024x+8x-1$$

Combine 13824x and -1024x to get 12800x.

$$12800x+8x-1$$

Combine 12800x and 8x to get 12808x.

$$12808x-1$$

Differentiate w.r.t. x

$$12808$$

Steps Using Derivative Rule for Sum

Calculate 24 to the power of 3 and get 13824.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13824x-32^{2}x+8x-1)$$

Calculate 32 to the power of 2 and get 1024.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13824x-1024x+8x-1)$$

Combine 13824x and -1024x to get 12800x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12800x+8x-1)$$

Combine 12800x and 8x to get 12808x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12808x-1)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$12808x^{1-1}$$

Subtract 1 from 1.

$$12808x^{0}$$

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

$$12808\times 1$$

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

$$12808$$