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Popular >

derivative of y^2-2xy+6x

Solution

\frac{d}{d x} (y^{2} - 2 x y + 6 x)

Solution

2 y \frac{d y}{d x} - 2 (y + x \frac{d y}{d x}) + 6

Solution steps

\frac{d}{d x} (y^{2} - 2 x y + 6 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (y^{2}) - \frac{d}{d x} (2 x y) + \frac{d}{d x} (6 x)

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

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

\frac{d}{d x} (6 x) = 6

= 2 y \frac{d y}{d x} - 2 (y + x \frac{d y}{d x}) + 6

Popular Examples

sum from k=0 to infinity of (1)^k

k = 0 \sum \infty (1)^{k}

integral of 1/(sqrt(2x^3))

\int \frac{1}{2 x ^{3}} d x

derivative of f(x)=\sqrt[3]{-(-27)}derivative of

f (x) = 3 - (- 27)

y^{''}+16y=tsin(4t)

y^{^{''}} + 16 y = t sin (4 t)

derivative of f(x)=(2x^2-1)^2(3x^2)derivative of

f (x) = (2 x^{2} - 1)^{2} (3 x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of y^2-2xy+6x ?
The derivative of y^2-2xy+6x is 2y(dy)/(dx)-2(y+x(dy)/(dx))+6
What is the first derivative of y^2-2xy+6x ?
The first derivative of y^2-2xy+6x is 2y(dy)/(dx)-2(y+x(dy)/(dx))+6