What is implicit (dy)/(dx),y= 6/(\sqrt[3]{x^2+5)} ?

The answer to implicit (dy)/(dx),y= 6/(\sqrt[3]{x^2+5)} is (dy)/(dx)=-(4x)/((x^2+5)^{4/3)}

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implicit (dy)/(dx),y= 6/(\sqrt[3]{x^2+5)}

implicit derivative

\frac{d y}{d x} = - \frac{4 x}{( x ^{2} + 5 ) ^{\frac{4}{3}}}

Solution steps

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = - \frac{4 x}{( x ^{2} + 5 ) ^{\frac{4}{3}}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{4 x}{( x ^{2} + 5 ) ^{\frac{4}{3}}}

\frac{d y}{d x} = - \frac{4 x}{( x ^{2} + 5 ) ^{\frac{4}{3}}}

\frac{d}{d x} (\frac{4}{x + 6})

f (x) = - 4 tan (x) - 1, at x = - \frac{π}{4}

\frac{\partial}{\partial x} (2 y^{6} + 4 y^{8} x^{3})

- \frac{9}{x}

f (x) = x^{3} - 3 x + 1, (3, 19)

What is implicit (dy)/(dx),y= 6/(\sqrt[3]{x^2+5)} ?
The answer to implicit (dy)/(dx),y= 6/(\sqrt[3]{x^2+5)} is (dy)/(dx)=-(4x)/((x^2+5)^{4/3)}