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Popular >

derivative of (x+y2+2y^2)

Solution

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

Solution

2 (1 + \frac{d y}{d x}) + 4 y \frac{d y}{d x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} ((x + y) \cdot 2) = 2 (1 + \frac{d y}{d x})

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

= 2 (1 + \frac{d y}{d x}) + 4 y \frac{d y}{d x}

Popular Examples

extreme f(x)=(2(x+7)^2)/(x+10)extreme points

f (x) = \frac{2 ( x + 7 ) ^{2}}{x + 10}

extreme (2x^2-5x+5)/(x-2)extreme points

\frac{2 x ^{2} - 5 x + 5}{x - 2}

extreme f(x)=2x^2-12x+20 extreme points

f (x) = 2 x^{2} - 12 x + 20

extreme f(x)=4sin^2(x),0<= x<= pi extreme points

f (x) = 4 sin^{2} (x), 0 \leq x \leq π

extreme f(x,y)=x^3+y^3-3x^2-9y^2-9x extreme points

f (x, y) = x^{3} + y^{3} - 3 x^{2} - 9 y^{2} - 9 x

Frequently Asked Questions (FAQ)

What is the derivative of (x+y2+2y^2) ?
The derivative of (x+y2+2y^2) is 2(1+(dy)/(dx))+4y(dy)/(dx)
What is the first derivative of (x+y2+2y^2) ?
The first derivative of (x+y2+2y^2) is 2(1+(dy)/(dx))+4y(dy)/(dx)