What is the d/(dy)(3xe^{-1/(y^3)}-20x^3) ?

The d/(dy)(3xe^{-1/(y^3)}-20x^3) is (9e^{-1/(y^3)}x)/(y^4)

What is the first d/(dy)(3xe^{-1/(y^3)}-20x^3) ?

The first d/(dy)(3xe^{-1/(y^3)}-20x^3) is (9e^{-1/(y^3)}x)/(y^4)

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\frac{d}{d y} (3 x e^{- \frac{1}{y ^{3}}} - 20 x^{3})

\frac{9 e ^{- \frac{1}{y ^{3}}} x}{y ^{4}}

Solution steps

\frac{d}{d y} (3 x e^{- \frac{1}{y ^{3}}} - 20 x^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d y} (3 x e^{- \frac{1}{y ^{3}}}) - \frac{d}{d y} (20 x^{3})

\frac{d}{d y} (3 x e^{- \frac{1}{y ^{3}}}) = \frac{9 x e ^{- \frac{1}{y ^{3}}}}{y ^{4}}

\frac{d}{d y} (20 x^{3}) = 0

= \frac{9 x e ^{- \frac{1}{y ^{3}}}}{y ^{4}} - 0

Simplify

= \frac{9 e ^{- \frac{1}{y ^{3}}} x}{y ^{4}}

f (x) = x - \frac{1}{x} + ln (x), at x = 1

y = 16 x sin (x), (\frac{π}{2}, 8 π)

\frac{\partial}{\partial y} (x ln (y + z))

\int \frac{3}{x - 3} d x

x^{2} - 10

What is the d/(dy)(3xe^{-1/(y^3)}-20x^3) ?
The d/(dy)(3xe^{-1/(y^3)}-20x^3) is (9e^{-1/(y^3)}x)/(y^4)
What is the first d/(dy)(3xe^{-1/(y^3)}-20x^3) ?
The first d/(dy)(3xe^{-1/(y^3)}-20x^3) is (9e^{-1/(y^3)}x)/(y^4)