Solve 4x^2-15x+94x^2-15x+9

$$4 x ^ { 2 } - 15 x + 94 x ^ { 2 } - 15 x + 9$$

Evaluate

$$98x^{2}-30x+9$$

Solution Steps

Combine 4x^{2} and 94x^{2} to get 98x^{2}.

$$98x^{2}-15x-15x+9$$

Combine -15x and -15x to get -30x.

$$98x^{2}-30x+9$$

Differentiate w.r.t. x

$$196x-30$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and 94x^{2} to get 98x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(98x^{2}-15x-15x+9)$$

Combine -15x and -15x to get -30x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(98x^{2}-30x+9)$$

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}.

$$2\times 98x^{2-1}-30x^{1-1}$$

Multiply 2 times 98.

$$196x^{2-1}-30x^{1-1}$$

Subtract 1 from 2.

$$196x^{1}-30x^{1-1}$$

Subtract 1 from 1.

$$196x^{1}-30x^{0}$$

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

$$196x-30x^{0}$$

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

$$196x-30$$