Solve 2x^2-28^2:4^2

$$2 x ^ { 2 } - 28 ^ { 2 } : 4 ^ { 2 }$$

Evaluate

$$2x^{2}-49$$

Solution Steps

Calculate 28 to the power of 2 and get 784.

$$2x^{2}-\frac{784}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$2x^{2}-\frac{784}{16}$$

Divide 784 by 16 to get 49.

$$2x^{2}-49$$

Differentiate w.r.t. x

$$4x$$

Steps Using Derivative Rule for Sum

Calculate 28 to the power of 2 and get 784.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-\frac{784}{4^{2}})$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-\frac{784}{16})$$

Divide 784 by 16 to get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-49)$$

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}.

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

Multiply 2 times 2.

$$4x^{2-1}$$

Subtract 1 from 2.

$$4x^{1}$$

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

$$4x$$