What is the derivative of y^5-3xy ?

The derivative of y^5-3xy is 5y^4(dy)/(dx)-3(y+x(dy)/(dx))

What is the first derivative of y^5-3xy ?

The first derivative of y^5-3xy is 5y^4(dy)/(dx)-3(y+x(dy)/(dx))

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\frac{d}{d x} (y^{5} - 3 x y)

5 y^{4} \frac{d y}{d x} - 3 (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (y^{5} - 3 x y)

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (y^{5}) = 5 y^{4} \frac{d y}{d x}

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

= 5 y^{4} \frac{d y}{d x} - 3 (y + x \frac{d y}{d x})

f (x) = 4 x^{2}, at x = 0

7 sin (4 t + 8)

\int \frac{1}{81 e ^{- 5 x} + e ^{5 x}} d x

\int_{0}^{5} y + 4 d y

What is the derivative of y^5-3xy ?
The derivative of y^5-3xy is 5y^4(dy)/(dx)-3(y+x(dy)/(dx))
What is the first derivative of y^5-3xy ?
The first derivative of y^5-3xy is 5y^4(dy)/(dx)-3(y+x(dy)/(dx))