Respuesta :
The value of [tex]\frac{d^{2}y }{dx^2}[/tex] for equation [tex]y^5=x^7[/tex] is [tex]\frac{14}{25x^{\frac{3}{5}} }[/tex].
What is the differential of function?
The differential in calculus reflects the main part of the change in a function y = f(x) as a function of changes in the independent variable. dy=f', dx, where f' is the derivative of f with respect to x and dx is an additional real variable, defines the differential dy.
How to find the value of [tex]\frac{d^{2}y }{dx^2}[/tex]?
Given [tex]y^5=x^7[/tex]
simplify the equation for y
[tex]y=x^{\frac{7}{5} }[/tex]
Now differentiate with respect to x.
[tex]\frac{dy}{dx}=\frac{7}{5}x^{\frac{2}{5} }[/tex]
Again differentiate with respect to x
[tex]\frac{d^{2}y }{dx^2}=\frac{14}{25}x^{\frac{-3}{5} }[/tex]
[tex]=\frac{14}{25x^{\frac{3}{5}} }[/tex]
Hence value is [tex]\frac{14}{25x^{\frac{3}{5}} }[/tex]
Learn more about differential here: https://brainly.com/question/24062595
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