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Popular >

(\partial)/(\partial x)(x^3+y^2-5xy)

Solution

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

Solution

3 x^{2} - 5 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (5 x y) = 5 y

= 3 x^{2} + 0 - 5 y

Simplify

= 3 x^{2} - 5 y

Popular Examples

4 y^{^{''}} - y^{^{'}} = 0

y^{'''}+y^{''}+y^'+y=0

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = 0

integral from 0 to 7 of (50x+20)

\int_{0}^{7} (50 x + 20) d x

derivative of sin(pix)

\frac{d}{d x} (sin (π x))

y^{''}+4y=3sec(2t)

y^{^{''}} + 4 y = 3 sec (2 t)

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(x^3+y^2-5xy) ?
The answer to (\partial)/(\partial x)(x^3+y^2-5xy) is 3x^2-5y