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Popular >

derivative of 5x^3y^4

Solution

\frac{d}{d x} (5 x^{3} y^{4})

Solution

5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})

Solution steps

\frac{d}{d x} (5 x^{3} y^{4})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{3} y^{4})

Apply the Product Rule:

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

f = x^{3}, g = y^{4}

= 5 (\frac{d}{d x} (x^{3}) y^{4} + \frac{d}{d x} (y^{4}) x^{3})

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

\frac{d}{d x} (y^{4}) = 4 y^{3} \frac{d y}{d x}

= 5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})

Popular Examples

((dy)/(dx))^2+2e^x(dy)/(dx)+e^{2x}=0

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

derivative of 11-x^2 derivative of

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\int \frac{x ^{2}}{( 9 - x ^{2} ) ^{\frac{3}{2}}} d x

integral from 1 to 1000 of (37)/(x^3)

\int_{1}^{1000} \frac{37}{x ^{3}} d x

derivative of (1/(y^2)-3/(y^4))(y+7y^3)derivative of

(\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 7 y^{3})

Frequently Asked Questions (FAQ)

What is the derivative of 5x^3y^4 ?
The derivative of 5x^3y^4 is 5(3x^2y^4+4y^3(dy)/(dx)x^3)
What is the first derivative of 5x^3y^4 ?
The first derivative of 5x^3y^4 is 5(3x^2y^4+4y^3(dy)/(dx)x^3)