Fungsi turunan dari 3x+1 per √x²+11.... Question from @Yeyemimi

October 2018 2 51 Report

Fungsi turunan dari 3x+1 per √x²+11

Brillianttt F(x) = u/v
f(x) = 3x+1 / √x²+11

u' = 3
v = √x²+11 = (x²+11)^1/2 maka
v' = 1/2 (x²+11)^-1/2 .2x = x / √x²+11

f '(x) = u'v - v'u / v²
   = 3(√x²+11) - x(3x+1)/(√x²+11) / x²+11
   = 3(x²+11) - (3x²+x) /    ( x²+11)(√x²+11)
   = 33 - x / x²√(x²+11) + 11√(x²+11)

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izharulhaq78 kok turunan x² + 11 = 2?

izharulhaq78 $\displaystyle f(x)=\frac{3x+1}{\sqrt{x^2+11}}\\\\u=3x+1\\u'=3\\v=\sqrt{x^2+11}\\v'=\frac{x}{\sqrt{x^2+11}}\\\\f'(x)=\frac{u'v-uv'}{v^2}\\f'(x)=\frac{3(\sqrt{x^2+11})-(3x+1)(\frac{x}{\sqrt{x^2+11}})}{\sqrt{x^2+11}^2}\\f'(x)=\frac{3\sqrt{x^2+11}-\frac{3x^2+x}{\sqrt{x^2+11}}}{x^2+11}$
$\displaystyle f'(x)=\frac{\frac{3(x^2+11)}{\sqrt{x^2+11}}-\frac{3x^2+x}{\sqrt{x^2+11}}}{x^2+11}\\f'(x)=\frac{\frac{3x^2+33-3x^2-x}{\sqrt{x^2+11}}}{x^2+11}\\f'(x)=\frac{\frac{33-x}{\sqrt{x^2+11}}}{x^2+11}\\\boxed{\boxed{f'(x)=\frac{33-x}{(x^2+11)\sqrt{x^2+11}}}}$

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Brillianttt ya mas....

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Fungsi turunan dari √x²+11

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