What is the derivative of (x(x+2y)/(1000000)) ?

The derivative of (x(x+2y)/(1000000)) is (x+x\frac{dy)/(dx)+y}{500000}

What is the first derivative of (x(x+2y)/(1000000)) ?

The first derivative of (x(x+2y)/(1000000)) is (x+x\frac{dy)/(dx)+y}{500000}

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\frac{d}{d x} (\frac{x ( x + 2 y )}{1000000})

\frac{x + x \frac{d y}{d x} + y}{500000}

Solution steps

\frac{d}{d x} (\frac{x ( x + 2 y )}{1000000})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{1000000} \frac{d}{d x} (x (x + 2 y))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x + 2 y

= \frac{1}{1000000} (\frac{d x}{d x} (x + 2 y) + \frac{d}{d x} (x + 2 y) x)

\frac{d x}{d x} = 1

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

= \frac{1}{1000000} (1 \cdot (x + 2 y) + (1 + 2 \frac{d y}{d x}) x)

Simplify

\frac{1}{1000000} (1 \cdot (x + 2 y) + (1 + 2 \frac{d y}{d x}) x) : \frac{x + x \frac{d y}{d x} + y}{500000}

= \frac{x + x \frac{d y}{d x} + y}{500000}

y = \frac{t}{( t - 9 ) ^{2}}

\int (\frac{5 x}{5} + \frac{5}{5 x}) d x

y^{^{''}} + y^{^{'}} - 12 y = 3 e^{2 x}

y^{^{''}} + 6 y^{^{'}} + 8 y = - 6 t e^{4 t}

\int_{1}^{2} \frac{1}{x ( x - 5 )} d x

What is the derivative of (x(x+2y)/(1000000)) ?
The derivative of (x(x+2y)/(1000000)) is (x+x\frac{dy)/(dx)+y}{500000}
What is the first derivative of (x(x+2y)/(1000000)) ?
The first derivative of (x(x+2y)/(1000000)) is (x+x\frac{dy)/(dx)+y}{500000}