<img src="https://tex.z-dn.net/?f=F%28x%29%3D%286%20%5Csqrt%7Bx%7D%20-2%29%285%20%5Csqrt%7Bx%7D%20%2B7%29" id="TexFormula1" titl

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4 years ago

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e="F(x)=(6 \sqrt{x} -2)(5 \sqrt{x} +7)" alt="F(x)=(6 \sqrt{x} -2)(5 \sqrt{x} +7)" align="absmiddle" class="latex-formula">

1 answer:

Anarel [89]4 years ago

8 0

$\bf f(x)=(6\sqrt{x}-2)(5\sqrt{x}+7)
\\\\\\
\cfrac{dy}{dx}=\stackrel{product~rule}{\left( 6\cdot \frac{1}{2}x^{-\frac{1}{2}} \right)(5x^{\frac{1}{2}}+7)~~+~~(6x^{\frac{1}{2}}-2)\left(5\cdot \frac{1}{2}x^{-\frac{1}{2}} \right)}
\\\\\\
\cfrac{dy}{dx}=\left(\cfrac{6}{2}\cdot \cfrac{1}{\sqrt{x}} \right)(5x^{\frac{1}{2}}+7)~~+~~2(3x^{\frac{1}{2}}-1)\left(\cfrac{5}{2}x^{-\frac{1}{2}} \right)$

$\bf \cfrac{dy}{dx}=\left(3\cdot \cfrac{1}{\sqrt{x}} \right)(5x^{\frac{1}{2}}+7)~~+~~2\cdot \cfrac{5}{2}(3x^{\frac{1}{2}}-1)\left(\cfrac{1}{\sqrt{x}} \right)
\\\\\\
\cfrac{dy}{dx}=\cfrac{3(5\sqrt{x}+7)}{\sqrt{x}}~~+~~\cfrac{5(3\sqrt{x}-1)}{\sqrt{x}}\\\\\\
\cfrac{dy}{dx}=\cfrac{15\sqrt{x}+21~~+~~15\sqrt{x}-5}{\sqrt{x}}
\\\\\\
\cfrac{dy}{dx}=\cfrac{30\sqrt{x}+16}{\sqrt{x}}$

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