What is Dy(3x-2y^2+8/(y^3)) ?

The solution to Dy(3x-2y^2+8/(y^3)) is (D(3y^3x-2y^5+8))/(y^2)

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simplify Dy(3x-2y^2+8/(y^3))

simplify

Dy (3 x - 2 y^{2} + \frac{8}{y ^{3}})

\frac{D ( 3 y ^{3} x - 2 y ^{5} + 8 )}{y ^{2}}

Solution steps

Dy (3 x - 2 y^{2} + \frac{8}{y ^{3}})

Join

3 x - 2 y^{2} + \frac{8}{y ^{3}} : \frac{3 x y ^{3} - 2 y ^{5} + 8}{y ^{3}}

= Dy \frac{3 x y ^{3} - 2 y ^{5} + 8}{y ^{3}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{Dy ( 3 x y ^{3} - 2 y ^{5} + 8 )}{y ^{3}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

y^{3} = y y^{2}

= \frac{Dy ( 3 x y ^{3} - 2 y ^{5} + 8 )}{y y ^{2}}

Cancel the common factor:

y

= \frac{D ( 3 x y ^{3} - 2 y ^{5} + 8 )}{y ^{2}}

= \frac{D ( 3 y ^{3} x - 2 y ^{5} + 8 )}{y ^{2}}

- \frac{1}{( x - 2 ) ^{2}}

\frac{( 2 x - 3 ) ( 3 x + 8 )}{( x - 6 ) ^{3}}

\frac{- \frac{12}{4} - 45}{24} - 2 (- 3 + 5 - 37 + 62 - 17)

\frac{( x + 1 ) ^{3}}{3}

lo g_{10} (\frac{y z ^{5}}{x ^{3}})

What is Dy(3x-2y^2+8/(y^3)) ?
The solution to Dy(3x-2y^2+8/(y^3)) is (D(3y^3x-2y^5+8))/(y^2)