Solve 2^2x-1+5x-1-17

$$2 ^ { 2 } x - 1 + 5 x - 1 - 17$$

Evaluate

$$9x-19$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$4x-1+5x-1-17$$

Combine 4x and 5x to get 9x.

$$9x-1-1-17$$

Subtract 1 from -1 to get -2.

$$9x-2-17$$

Subtract 17 from -2 to get -19.

$$9x-19$$

Differentiate w.r.t. x

$$9$$

Steps Using Derivative Rule for Sum

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-1+5x-1-17)$$

Combine 4x and 5x to get 9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-1-1-17)$$

Subtract 1 from -1 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-2-17)$$

Subtract 17 from -2 to get -19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-19)$$

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}.

$$9x^{1-1}$$

Subtract 1 from 1.

$$9x^{0}$$

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

$$9\times 1$$

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

$$9$$