What is the derivative of (x-2^2sqrt(-3x)) ?

The derivative of (x-2^2sqrt(-3x)) is (sqrt(3)(-5x^2+12x-4))/(2sqrt(-x))

What is the first derivative of (x-2^2sqrt(-3x)) ?

The first derivative of (x-2^2sqrt(-3x)) is (sqrt(3)(-5x^2+12x-4))/(2sqrt(-x))

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\frac{d}{d x} ((x - 2)^{2} - 3 x)

\frac{3 ( - 5 x ^{2} + 12 x - 4 )}{2 - x}

Solution steps

\frac{d}{d x} ((x - 2)^{2} - 3 x)

Simplify

(x - 2)^{2} - 3 x : 3 (x - 2)^{2} - x

= \frac{d}{d x} (3 (x - 2)^{2} - x)

Take the constant out:

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

= 3 \frac{d}{d x} ((x - 2)^{2} - x)

Apply the Product Rule:

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

f = (x - 2)^{2}, g = - x

= 3 (\frac{d}{d x} ((x - 2)^{2}) - x + \frac{d}{d x} (- x) (x - 2)^{2})

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

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

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

Simplify

3 (2 (x - 2) - x + (- \frac{1}{2 - x}) (x - 2)^{2}) : \frac{3 ( - 5 x ^{2} + 12 x - 4 )}{2 - x}

= \frac{3 ( - 5 x ^{2} + 12 x - 4 )}{2 - x}

What is the derivative of (x-2^2sqrt(-3x)) ?
The derivative of (x-2^2sqrt(-3x)) is (sqrt(3)(-5x^2+12x-4))/(2sqrt(-x))
What is the first derivative of (x-2^2sqrt(-3x)) ?
The first derivative of (x-2^2sqrt(-3x)) is (sqrt(3)(-5x^2+12x-4))/(2sqrt(-x))