What is the derivative of x^3sin(y^3) ?

The derivative of x^3sin(y^3) is 3x^2sin(y^3)+cos(y^3)*3y^2(dy)/(dx)x^3

What is the first derivative of x^3sin(y^3) ?

The first derivative of x^3sin(y^3) is 3x^2sin(y^3)+cos(y^3)*3y^2(dy)/(dx)x^3

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

3 x^{2} sin (y^{3}) + cos (y^{3}) \cdot 3 y^{2} \frac{d y}{d x} x^{3}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = sin (y^{3})

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

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

\frac{d}{d x} (sin (y^{3})) = cos (y^{3}) \cdot 3 y^{2} \frac{d y}{d x}

= 3 x^{2} sin (y^{3}) + cos (y^{3}) \cdot 3 y^{2} \frac{d y}{d x} x^{3}

y = sin (e^{2} x)

x^{x} - 2^{s} in x

- 0.25 x

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

lo g_{10} (x^{2} + 3)

What is the derivative of x^3sin(y^3) ?
The derivative of x^3sin(y^3) is 3x^2sin(y^3)+cos(y^3)*3y^2(dy)/(dx)x^3
What is the first derivative of x^3sin(y^3) ?
The first derivative of x^3sin(y^3) is 3x^2sin(y^3)+cos(y^3)*3y^2(dy)/(dx)x^3