Solve d/dxleft(2/3*(x+5)*(x+5)right)

$$\frac{d}{d x } \left( \frac{ 2 }{ 3 } \times (x+5) \times (x+5) \right)$$

Evaluate

$$\frac{4\left(x+5\right)}{3}$$

Steps Using Derivative Rule for Sum

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}\left(x+5\right)^{2})$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}\left(x^{2}+10x+25\right))$$

Use the distributive property to multiply \frac{2}{3} by x^{2}+10x+25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{2}+\frac{2}{3}\times 10x+\frac{2}{3}\times 25)$$

Express \frac{2}{3}\times 10 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{2}+\frac{2\times 10}{3}x+\frac{2}{3}\times 25)$$

Multiply 2 and 10 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{2}+\frac{20}{3}x+\frac{2}{3}\times 25)$$

Express \frac{2}{3}\times 25 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{2}+\frac{20}{3}x+\frac{2\times 25}{3})$$

Multiply 2 and 25 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{2}+\frac{20}{3}x+\frac{50}{3})$$

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}.

$$2\times \frac{2}{3}x^{2-1}+\frac{20}{3}x^{1-1}$$

Multiply 2 times \frac{2}{3}.

$$\frac{4}{3}x^{2-1}+\frac{20}{3}x^{1-1}$$

Subtract 1 from 2.

$$\frac{4}{3}x^{1}+\frac{20}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{4}{3}x^{1}+\frac{20}{3}x^{0}$$

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

$$\frac{4}{3}x+\frac{20}{3}x^{0}$$

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

$$\frac{4}{3}x+\frac{20}{3}\times 1$$

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

$$\frac{4}{3}x+\frac{20}{3}$$

Differentiate w.r.t. x

$$\frac{4}{3} = 1\frac{1}{3} = 1.3333333333333333$$