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Apply the formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right)$, where $a=\frac{1}{2}$ and $x=\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}$
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$\frac{1}{2}\left(\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}\right)^{-\frac{1}{2}}\frac{d}{dx}\left(\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}\right)$
Learn how to solve problems step by step online. d/dx(((x(x+2))/((2x+1)(5x+3)))^(1/2)). Apply the formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), where a=\frac{1}{2} and x=\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}. Apply the formula: \left(\frac{a}{b}\right)^n=\left(\frac{b}{a}\right)^{\left|n\right|}, where a=x\left(x+2\right), b=\left(2x+1\right)\left(5x+3\right) and n=-\frac{1}{2}. Apply the formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, where a=x\left(x+2\right) and b=\left(2x+1\right)\left(5x+3\right). Apply the formula: \left(ab\right)^n=a^nb^n.
