Solve 6x^2-x+5-7+6^2

$$6 x ^ { 2 } - x + 5 - 7 + 6 ^ { 2 }$$

Evaluate

$$6x^{2}-x+34$$

Solution Steps

Subtract 7 from 5 to get -2.

$$6x^{2}-x-2+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$6x^{2}-x-2+36$$

Add -2 and 36 to get 34.

$$6x^{2}-x+34$$

Differentiate w.r.t. x

$$12x-1$$

Steps Using Derivative Rule for Sum

Subtract 7 from 5 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}-x-2+6^{2})$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}-x-2+36)$$

Add -2 and 36 to get 34.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}-x+34)$$

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}.

$$2\times 6x^{2-1}-x^{1-1}$$

Multiply 2 times 6.

$$12x^{2-1}-x^{1-1}$$

Subtract 1 from 2.

$$12x^{1}-x^{1-1}$$

Subtract 1 from 1.

$$12x^{1}-x^{0}$$

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

$$12x-x^{0}$$

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

$$12x-1$$