What is (\partial)/(\partial x)(3x^2+5xy-7y^2+1) ?

The answer to (\partial)/(\partial x)(3x^2+5xy-7y^2+1) is 6x+5y

Popular >

(\partial)/(\partial x)(3x^2+5xy-7y^2+1)

\frac{\partial}{\partial x} (3 x^{2} + 5 x y - 7 y^{2} + 1)

6 x + 5 y

Solution steps

\frac{\partial}{\partial x} (3 x^{2} + 5 x y - 7 y^{2} + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (5 x y) - \frac{\partial}{\partial x} (7 y^{2}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

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

\frac{\partial}{\partial x} (7 y^{2}) = 0

\frac{\partial}{\partial x} (1) = 0

= 6 x + 5 y - 0 + 0

Simplify

= 6 x + 5 y

\frac{d}{d x} (e^{x^{2} + 4})

\int x^{2} (6 - x^{3}) d x

\frac{d}{d x} (cos^{2} (2 x + 1))

\int \frac{3}{5} d x

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 2 yz)

What is (\partial)/(\partial x)(3x^2+5xy-7y^2+1) ?
The answer to (\partial)/(\partial x)(3x^2+5xy-7y^2+1) is 6x+5y