Solve 10x^2-6x+1-5x+7+8x^2-4x

$$10 { x }^{ 2 } -6x+1-5x+7+8 { x }^{ 2 } -4x$$

Evaluate

$$18x^{2}-15x+8$$

Solution Steps

Combine -6x and -5x to get -11x.

$$10x^{2}-11x+1+7+8x^{2}-4x$$

Add 1 and 7 to get 8.

$$10x^{2}-11x+8+8x^{2}-4x$$

Combine 10x^{2} and 8x^{2} to get 18x^{2}.

$$18x^{2}-11x+8-4x$$

Combine -11x and -4x to get -15x.

$$18x^{2}-15x+8$$

Differentiate w.r.t. x

$$36x-15$$

Steps Using Derivative Rule for Sum

Combine -6x and -5x to get -11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}-11x+1+7+8x^{2}-4x)$$

Add 1 and 7 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}-11x+8+8x^{2}-4x)$$

Combine 10x^{2} and 8x^{2} to get 18x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{2}-11x+8-4x)$$

Combine -11x and -4x to get -15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{2}-15x+8)$$

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}.

$$2\times 18x^{2-1}-15x^{1-1}$$

Multiply 2 times 18.

$$36x^{2-1}-15x^{1-1}$$

Subtract 1 from 2.

$$36x^{1}-15x^{1-1}$$

Subtract 1 from 1.

$$36x^{1}-15x^{0}$$

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

$$36x-15x^{0}$$

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

$$36x-15$$