Solve (5x^2-4x+3)+(3x^2+4x-3)=

$$( 5 x ^ { 2 } - 4 x + 3 ) + ( 3 x ^ { 2 } + 4 x - 3 ) =$$

Evaluate

$$8x^{2}$$

Solution Steps

Combine 5x^{2} and 3x^{2} to get 8x^{2}.

$$8x^{2}-4x+3+4x-3$$

Combine -4x and 4x to get 0.

$$8x^{2}+3-3$$

Subtract 3 from 3 to get 0.

$$8x^{2}$$

Differentiate w.r.t. x

$$16x$$

Steps Using Definition of a Derivative

Combine 5x^{2} and 3x^{2} to get 8x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2}-4x+3+4x-3)$$

Combine -4x and 4x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2}+3-3)$$

Subtract 3 from 3 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2})$$

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

$$2\times 8x^{2-1}$$

Multiply 2 times 8.

$$16x^{2-1}$$

Subtract 1 from 2.

$$16x^{1}$$

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

$$16x$$