What is the derivative of x^4+5xy^3 ?

The derivative of x^4+5xy^3 is 4x^3+5(y^3+3xy^2(dy)/(dx))

What is the first derivative of x^4+5xy^3 ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\int \frac{2}{t} d t

g (x) = \frac{x ^{2} - 4}{x - 2}

x (x - 3)

\int_{0}^{\frac{5}{2}} 25 - x^{2} d x

\int (9 - x) d x

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