Solve 16x^2+24xx+9x^2

$$16 { x }^{ 2 } +24xx+9 { x }^{ 2 }$$

Evaluate

$$49x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$16x^{2}+24x^{2}+9x^{2}$$

Combine 16x^{2} and 24x^{2} to get 40x^{2}.

$$40x^{2}+9x^{2}$$

Combine 40x^{2} and 9x^{2} to get 49x^{2}.

$$49x^{2}$$

Differentiate w.r.t. x

$$98x$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{2}+24x^{2}+9x^{2})$$

Combine 16x^{2} and 24x^{2} to get 40x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(40x^{2}+9x^{2})$$

Combine 40x^{2} and 9x^{2} to get 49x^{2}.

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

The derivative of ax^{n} is nax^{n-1}.

$$2\times 49x^{2-1}$$

Multiply 2 times 49.

$$98x^{2-1}$$

Subtract 1 from 2.

$$98x^{1}$$

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

$$98x$$