Solve 25x^2-70x+49+x^2+8x+16

$$25 { x }^{ 2 } -70x+49+ { x }^{ 2 } +8x+16$$

Evaluate

$$26x^{2}-62x+65$$

Solution Steps

Combine 25x^{2} and x^{2} to get 26x^{2}.

$$26x^{2}-70x+49+8x+16$$

Combine -70x and 8x to get -62x.

$$26x^{2}-62x+49+16$$

Add 49 and 16 to get 65.

$$26x^{2}-62x+65$$

Differentiate w.r.t. x

$$52x-62$$

Steps Using Derivative Rule for Sum

Combine 25x^{2} and x^{2} to get 26x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(26x^{2}-70x+49+8x+16)$$

Combine -70x and 8x to get -62x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(26x^{2}-62x+49+16)$$

Add 49 and 16 to get 65.

$$\frac{\mathrm{d}}{\mathrm{d}x}(26x^{2}-62x+65)$$

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}.

$$2\times 26x^{2-1}-62x^{1-1}$$

Multiply 2 times 26.

$$52x^{2-1}-62x^{1-1}$$

Subtract 1 from 2.

$$52x^{1}-62x^{1-1}$$

Subtract 1 from 1.

$$52x^{1}-62x^{0}$$

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

$$52x-62x^{0}$$

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

$$52x-62$$