What is the derivative of i*x*sqrt(1-2x) ?

The derivative of i*x*sqrt(1-2x) is i((1-3x)sqrt(1-2x))/(1-2x)

What is the first derivative of i*x*sqrt(1-2x) ?

The first derivative of i*x*sqrt(1-2x) is i((1-3x)sqrt(1-2x))/(1-2x)

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\frac{d}{d x} (i \cdot x \cdot 1 - 2 x)

i \frac{( 1 - 3 x ) 1 - 2 x}{1 - 2 x}

Solution steps

\frac{d}{d x} (i x 1 - 2 x)

Take the constant out:

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

= i \frac{d}{d x} (x 1 - 2 x)

Apply the Product Rule:

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

f = x, g = 1 - 2 x

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

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

\frac{d}{d x} (1 - 2 x) = - \frac{1}{1 - 2 x}

= i (1 \cdot 1 - 2 x + (- \frac{1}{1 - 2 x}) x)

Simplify

i (1 \cdot 1 - 2 x + (- \frac{1}{1 - 2 x}) x) : i \frac{( 1 - 3 x ) 1 - 2 x}{1 - 2 x}

= i \frac{( 1 - 3 x ) 1 - 2 x}{1 - 2 x}

4 x^{2} y + 1

3^{5 x^{2}}

\frac{d}{d t} (20 sin (2 t - 3 x))

y = 3 x^{7}

2 y^{2} + 1

What is the derivative of i*x*sqrt(1-2x) ?
The derivative of i*x*sqrt(1-2x) is i((1-3x)sqrt(1-2x))/(1-2x)
What is the first derivative of i*x*sqrt(1-2x) ?
The first derivative of i*x*sqrt(1-2x) is i((1-3x)sqrt(1-2x))/(1-2x)