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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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