What is the derivative of x^3(ln(+1e^y)) ?

The derivative of x^3(ln(+1e^y)) is 3x^2y+(dy)/(dx)x^3

What is the first derivative of x^3(ln(+1e^y)) ?

The first derivative of x^3(ln(+1e^y)) is 3x^2y+(dy)/(dx)x^3

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\frac{d}{d x} (x^{3} (ln (+ 1 e^{y})))

3 x^{2} y + \frac{d y}{d x} x^{3}

Solution steps

\frac{d}{d x} (x^{3} (ln (1 \cdot e^{y})))

Simplify

x^{3} (ln (1 \cdot e^{y})) : x^{3} y

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

Apply the Product Rule:

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

f = x^{3}, g = y

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 3 x^{2} y + \frac{d y}{d x} x^{3}

\frac{d}{d x} ((\frac{x + 1}{x})^{\frac{3}{7}})

f (x) = 2 x^{9} + 5 x

1 + cot (x)

sin (\frac{1}{z})

(1 + x)^{3} (1 - x)^{7}

What is the derivative of x^3(ln(+1e^y)) ?
The derivative of x^3(ln(+1e^y)) is 3x^2y+(dy)/(dx)x^3
What is the first derivative of x^3(ln(+1e^y)) ?
The first derivative of x^3(ln(+1e^y)) is 3x^2y+(dy)/(dx)x^3