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Popular >

derivative of 5x^3y

Solution

\frac{d}{d x} (5 x^{3} y)

Solution

5 (3 x^{2} y + \frac{d y}{d x} x^{3})

Solution steps

\frac{d}{d x} (5 x^{3} y)

Take the constant out:

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

= 5 \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

= 5 (\frac{d}{d x} (x^{3}) y + \frac{d y}{d x} x^{3})

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

= 5 (3 x^{2} y + \frac{d y}{d x} x^{3})

Popular Examples

derivative of (tsin(t))/(1+t)derivative of

\frac{t sin ( t )}{1 + t}

area x/(1+x^2),((x^2))/(1+x^3)area

\frac{x}{1 + x ^{2}}, \frac{( x ^{2} )}{1 + x ^{3}}

y^'=(xy+2y)/(x+3)

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

x(x^3+1)y^'+(2x^3-1)y=(x^3-2)/x

x (x^{3} + 1) y^{^{'}} + (2 x^{3} - 1) y = \frac{x ^{3} - 2}{x}

integral of sqrt(x^2-49)

\int x^{2} - 49 d x

Frequently Asked Questions (FAQ)

What is the derivative of 5x^3y ?
The derivative of 5x^3y is 5(3x^2y+(dy)/(dx)x^3)
What is the first derivative of 5x^3y ?
The first derivative of 5x^3y is 5(3x^2y+(dy)/(dx)x^3)