What is the derivative of x,x^2-y,x+y^2 ?

The derivative of x,x^2-y,x+y^2 is (,(1*x^2+2xx))-(,((dy)/(dx)x+1*y))+2y(dy)/(dx)

What is the first derivative of x,x^2-y,x+y^2 ?

The first derivative of x,x^2-y,x+y^2 is (,(1*x^2+2xx))-(,((dy)/(dx)x+1*y))+2y(dy)/(dx)

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\frac{d}{d x} (x, x^{2} - y, x + y^{2})

(, (1 \cdot x^{2} + 2 xx)) - (, (\frac{d y}{d x} x + 1 \cdot y)) + 2 y \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x, x^{2} - y, x + y^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x, x^{2}) - \frac{d}{d x} (y, x) + \frac{d}{d x} (y^{2})

\frac{d}{d x} (x, x^{2}) = (, (1 \cdot x^{2} + 2 xx))

\frac{d}{d x} (y, x) = (, (\frac{d y}{d x} x + 1 \cdot y))

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

= (, (1 \cdot x^{2} + 2 xx)) - (, (\frac{d y}{d x} x + 1 \cdot y)) + 2 y \frac{d y}{d x}

\int \frac{5}{( 8 z - 1 ) ^{\frac{7}{8}}} d z

e^{2} + ln (4)

x \to 0 - lim (\frac{1}{x})

x \to 2 lim (\frac{x - 2}{4 - x ^{2}})

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

What is the derivative of x,x^2-y,x+y^2 ?
The derivative of x,x^2-y,x+y^2 is (,(1*x^2+2xx))-(,((dy)/(dx)x+1*y))+2y(dy)/(dx)
What is the first derivative of x,x^2-y,x+y^2 ?
The first derivative of x,x^2-y,x+y^2 is (,(1*x^2+2xx))-(,((dy)/(dx)x+1*y))+2y(dy)/(dx)