What is implicit (d^2y)/(dx^2),y=\sqrt[7]{x} ?

The answer to implicit (d^2y)/(dx^2),y=\sqrt[7]{x} is (d^2y)/(dx^2)=-6/(49x^{13/7)}

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implicit (d^2y)/(dx^2),y=\sqrt[7]{x}

implicit derivative

\frac{d ^{2} y}{d x ^{2}} = - \frac{6}{49 x ^{\frac{13}{7}}}

Solution steps

Treat

y

y (x)

Implicit Derivative

\frac{d y}{d x}

\frac{d y}{d x} = \frac{1}{7 x ^{\frac{6}{7}}}

Implicit Derivative

\frac{d ^{2} y}{d x ^{2}}

\frac{d y}{d x} = \frac{1}{7 x ^{\frac{6}{7}}} : - \frac{6}{49 x ^{\frac{13}{7}}}

\frac{d ^{2} y}{d x ^{2}} = - \frac{6}{49 x ^{\frac{13}{7}}}

Substitute

\frac{d y}{d x} = \frac{1}{7 x ^{\frac{6}{7}}} : - \frac{6}{49 x ^{\frac{13}{7}}}

\frac{d ^{2} y}{d x ^{2}} = - \frac{6}{49 x ^{\frac{13}{7}}}

\int tan (x) + 2 cot (x) d x

\int \frac{sec ( 7 x )}{7} d x

\int \frac{1}{100 x - x ^{2}} d x

\int (5 x^{3} - 7 x^{2} + 3 x + 4) d x

y = x^{2} + 5

What is implicit (d^2y)/(dx^2),y=\sqrt[7]{x} ?
The answer to implicit (d^2y)/(dx^2),y=\sqrt[7]{x} is (d^2y)/(dx^2)=-6/(49x^{13/7)}