What is the derivative of In(x^2y) ?

The derivative of In(x^2y) is In(2xy(I,x)+derivative of y(I,x)x^2)

What is the first derivative of In(x^2y) ?

The first derivative of In(x^2y) is In(2xy(I,x)+derivative of y(I,x)x^2)

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\frac{d}{d x} (I n (x^{2} y (I, x)))

I n (2 x y (I, x) + \frac{d}{d x} (y (I, x)) x^{2})

Solution steps

\frac{d}{d x} (I n (x^{2} y (I, x)))

Treat

n, I

as a constant

Take the constant out:

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

= I n \frac{d}{d x} (x^{2} y (I, x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = y (I, x)

= I n (\frac{d}{d x} (x^{2}) y (I, x) + \frac{d}{d x} (y (I, x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= I n (2 x y (I, x) + \frac{d}{d x} (y (I, x)) x^{2})

\frac{( x ^{2} + 1 ) d y}{d x} + x y - x = 0

e^{2 t} sin (2 t)

S^{2}

\int sin (t) \cdot cos (t) d t

x \to 2 lim (3 x^{2} + 2 x)

What is the derivative of In(x^2y) ?
The derivative of In(x^2y) is In(2xy(I,x)+derivative of y(I,x)x^2)
What is the first derivative of In(x^2y) ?
The first derivative of In(x^2y) is In(2xy(I,x)+derivative of y(I,x)x^2)