What is the derivative of (1/5)(xy^2+4y)^2 ?

The derivative of (1/5)(xy^2+4y)^2 is (2y^2(xy^2+4y))/5

What is the first derivative of (1/5)(xy^2+4y)^2 ?

The first derivative of (1/5)(xy^2+4y)^2 is (2y^2(xy^2+4y))/5

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derivative of

(\frac{1}{5}) (x y^{2} + 4 y)^{2}

\frac{2 y ^{2} ( x y ^{2} + 4 y )}{5}

Solution steps

\frac{d}{d x} (\frac{1}{5} (x y^{2} + 4 y)^{2})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} ((x y^{2} + 4 y)^{2})

Apply the chain rule:

2 (x y^{2} + 4 y) \frac{d}{d x} (x y^{2} + 4 y)

= 2 (x y^{2} + 4 y) \frac{d}{d x} (x y^{2} + 4 y)

\frac{d}{d x} (x y^{2} + 4 y) = y^{2}

= \frac{1}{5} \cdot 2 (x y^{2} + 4 y) y^{2}

Simplify

\frac{1}{5} \cdot 2 (x y^{2} + 4 y) y^{2} : \frac{2 y ^{2} ( x y ^{2} + 4 y )}{5}

= \frac{2 y ^{2} ( x y ^{2} + 4 y )}{5}

\int x \cdot cos (x) d x

\frac{d}{d x} (ln (x^{3}) + e^{2 x})

\frac{d y}{d x} = 7 y \cdot e^{(x + 9)}

\int \frac{e ^{x}}{( e ^{x} - 3 ) ( e ^{x} + 2 )} d x

f (x) = csc^{7} (2 x^{π} + π^{3})

What is the derivative of (1/5)(xy^2+4y)^2 ?
The derivative of (1/5)(xy^2+4y)^2 is (2y^2(xy^2+4y))/5
What is the first derivative of (1/5)(xy^2+4y)^2 ?
The first derivative of (1/5)(xy^2+4y)^2 is (2y^2(xy^2+4y))/5