What is implicit (dy)/(dx),y=x^pi ?

The answer to implicit (dy)/(dx),y=x^pi is (dy)/(dx)=pix^{pi-1}

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implicit (dy)/(dx),y=x^pi

implicit derivative

\frac{d y}{d x}, y = x^{π}

\frac{d y}{d x} = π x^{π - 1}

Solution steps

y = x^{π}

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = π x^{π - 1}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = π x^{π - 1}

\frac{d y}{d x} = π x^{π - 1}

t y^{^{'}} + t^{2} + t y - y = 0

h \to 0 lim (\frac{( 1 + h ) ^{9} - 1}{h})

\frac{d}{d x} (x^{3} + 6 x^{2})

5 x y (\frac{d y}{d x}) = 3

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