Solve 10/x*3/x+10*2/x+1

$$\frac{ 10 }{ x } \times \frac{ 3 }{ x+10 } \times \frac{ 2 }{ x+1 }$$

Evaluate

$$\frac{60}{x\left(x+1\right)\left(x+10\right)}$$

Solution Steps

Multiply \frac{10}{x} times \frac{3}{x+10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 3}{x\left(x+10\right)}\times \frac{2}{x+1}$$

Multiply \frac{10\times 3}{x\left(x+10\right)} times \frac{2}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 3\times 2}{x\left(x+10\right)\left(x+1\right)}$$

Multiply 10 and 3 to get 30.

$$\frac{30\times 2}{x\left(x+10\right)\left(x+1\right)}$$

Multiply 30 and 2 to get 60.

$$\frac{60}{x\left(x+10\right)\left(x+1\right)}$$

Use the distributive property to multiply x by x+10.

$$\frac{60}{\left(x^{2}+10x\right)\left(x+1\right)}$$

Apply the distributive property by multiplying each term of x^{2}+10x by each term of x+1.

$$\frac{60}{x^{3}+x^{2}+10x^{2}+10x}$$

Combine x^{2} and 10x^{2} to get 11x^{2}.

$$\frac{60}{x^{3}+11x^{2}+10x}$$

Differentiate w.r.t. x

$$-\frac{20\left(\left(3x+11\right)^{2}-91\right)}{\left(x\left(x+1\right)\left(x+10\right)\right)^{2}}$$