Solve 7x^2+45x-12sqrt{4}

$$7 { x }^{ 2 } +45x-12 \sqrt{ 4 }$$

Evaluate

$$7x^{2}+45x-24$$

Solution Steps

Calculate the square root of 4 and get 2.

$$7x^{2}+45x-12\times 2$$

Multiply -12 and 2 to get -24.

$$7x^{2}+45x-24$$

Differentiate w.r.t. x

$$14x+45$$

Steps Using Derivative Rule for Sum

Calculate the square root of 4 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+45x-12\times 2)$$

Multiply -12 and 2 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+45x-24)$$

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}.

$$2\times 7x^{2-1}+45x^{1-1}$$

Multiply 2 times 7.

$$14x^{2-1}+45x^{1-1}$$

Subtract 1 from 2.

$$14x^{1}+45x^{1-1}$$

Subtract 1 from 1.

$$14x^{1}+45x^{0}$$

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

$$14x+45x^{0}$$

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

$$14x+45\times 1$$

For any term t, t\times 1=t and 1t=t.

$$14x+45$$