Solve 4x^2-5x+27+(3x^2-4x-7)

$$4 x ^ { 2 } - 5 x + 27 + ( 3 x ^ { 2 } - 4 x - 7 )$$

Evaluate

$$7x^{2}-9x+20$$

Solution Steps

Combine 4x^{2} and 3x^{2} to get 7x^{2}.

$$7x^{2}-5x+27-4x-7$$

Combine -5x and -4x to get -9x.

$$7x^{2}-9x+27-7$$

Subtract 7 from 27 to get 20.

$$7x^{2}-9x+20$$

Differentiate w.r.t. x

$$14x-9$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and 3x^{2} to get 7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-5x+27-4x-7)$$

Combine -5x and -4x to get -9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-9x+27-7)$$

Subtract 7 from 27 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-9x+20)$$

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}.

$$2\times 7x^{2-1}-9x^{1-1}$$

Multiply 2 times 7.

$$14x^{2-1}-9x^{1-1}$$

Subtract 1 from 2.

$$14x^{1}-9x^{1-1}$$

Subtract 1 from 1.

$$14x^{1}-9x^{0}$$

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

$$14x-9x^{0}$$

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

$$14x-9$$