Question

$$\frac{ \displaystyle\frac{d}{d x } \left(12 \frac{ 6 }{ 9 } \right) }{ 5x } + \frac{ \sqrt{ 925 \times 2 } }{ 93+z2 } =$$

Answer

$$(25*sqrt(74)*x+IM*d*f^2*x,8*(93+2*z))/(5*x*(93+2*z))$$

Solution


Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{d\imath ff(x,\frac{12\times 6}{9})}{5x}+\frac{\sqrt{925\times 2}}{93+z\times 2}\]
Simplify  \(12\times 6\)  to  \(72\).
\[\frac{d\imath ff(x,\frac{72}{9})}{5x}+\frac{\sqrt{925\times 2}}{93+z\times 2}\]
Simplify  \(\frac{72}{9}\)  to  \(8\).
\[\frac{d\imath ff(x,8)}{5x}+\frac{\sqrt{925\times 2}}{93+z\times 2}\]
Simplify  \(d\imath ff(x,8)\)  to  \(d\imath ffx,8\).
\[\frac{d\imath ffx,8}{5x}+\frac{\sqrt{925\times 2}}{93+z\times 2}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{d\imath {f}^{2}x,8}{5x}+\frac{\sqrt{925\times 2}}{93+z\times 2}\]
Regroup terms.
\[\frac{\imath d{f}^{2}x,8}{5x}+\frac{\sqrt{925\times 2}}{93+z\times 2}\]
Simplify  \(925\times 2\)  to  \(1850\).
\[\frac{\imath d{f}^{2}x,8}{5x}+\frac{\sqrt{1850}}{93+z\times 2}\]
Simplify  \(\sqrt{1850}\)  to  \(5\sqrt{74}\).
\[\frac{\imath d{f}^{2}x,8}{5x}+\frac{5\sqrt{74}}{93+z\times 2}\]
Regroup terms.
\[\frac{\imath d{f}^{2}x,8}{5x}+\frac{5\sqrt{74}}{93+2z}\]
Regroup terms.
\[\frac{5\sqrt{74}}{93+2z}+\frac{\imath d{f}^{2}x,8}{5x}\]
Rewrite the expression with a common denominator.
\[\frac{5\sqrt{74}\times 5x+\imath d{f}^{2}x,8(93+2z)}{(93+2z)\times 5x}\]
Simplify  \(5\sqrt{74}\times 5x\)  to  \(25x\sqrt{74}\).
\[\frac{25x\sqrt{74}+\imath d{f}^{2}x,8(93+2z)}{(93+2z)\times 5x}\]
Regroup terms.
\[\frac{25\sqrt{74}x+\imath d{f}^{2}x,8(93+2z)}{(93+2z)\times 5x}\]
Regroup terms.
\[\frac{25\sqrt{74}x+\imath d{f}^{2}x,8(93+2z)}{5x(93+2z)}\]