Solve 25x^2+10xdiv5x

$$25 { x }^{ 2 } +10x \div 5x$$

Evaluate

$$27x^{2}$$

Solution Steps

Divide 10x by 5 to get 2x.

$$25x^{2}+2xx$$

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

$$25x^{2}+2x^{2}$$

Combine 25x^{2} and 2x^{2} to get 27x^{2}.

$$27x^{2}$$

Differentiate w.r.t. x

$$54x$$

Steps Using Definition of a Derivative

Divide 10x by 5 to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{2}+2xx)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{2}+2x^{2})$$

Combine 25x^{2} and 2x^{2} to get 27x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{2})$$

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

$$2\times 27x^{2-1}$$

Multiply 2 times 27.

$$54x^{2-1}$$

Subtract 1 from 2.

$$54x^{1}$$

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

$$54x$$