What is implicit (dy)/(dx),x=y^{18} ?

The answer to implicit (dy)/(dx),x=y^{18} is (dy)/(dx)= 1/(18y^{17)}

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implicit (dy)/(dx),x=y^{18}

implicit derivative

\frac{d y}{d x}, x = y^{18}

\frac{d y}{d x} = \frac{1}{18 y ^{17}}

Solution steps

x = y^{18}

Treat

y

y (x)

Differentiate both sides:

1 = 18 y^{17} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{18 y ^{17}}

\frac{d y}{d x} = \frac{1}{18 y ^{17}}

g (x) = 1 - x

y^{^{''}} + y = 0, y (0) = 1, y^{^{'}} (0) = 0

x y^{^{''}} + y^{^{'}} = 20 x

\frac{\partial}{\partial y} (e^{2 x y^{2}} + 3 x)

\int 5 x^{2} ln (x) d x

What is implicit (dy)/(dx),x=y^{18} ?
The answer to implicit (dy)/(dx),x=y^{18} is (dy)/(dx)= 1/(18y^{17)}