What is the derivative of f(x)=x^2sqrt(x-5x) ?

The derivative of f(x)=x^2sqrt(x-5x) is -(5x^2)/(sqrt(-x))

What is the first derivative of f(x)=x^2sqrt(x-5x) ?

The first derivative of f(x)=x^2sqrt(x-5x) is -(5x^2)/(sqrt(-x))

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derivative of

f (x) = x^{2} x - 5 x

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

Solution steps

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

Simplify

x^{2} x - 5 x : 2 x^{2} - x

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{1 - 5 x}{3 + x})

\frac{\partial}{\partial x} (x arctan (\frac{y}{z}))

f (r) = e^{r} + x^{e}

0.1 x^{3} - 0.1 x^{2} + 50 x

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

What is the derivative of f(x)=x^2sqrt(x-5x) ?
The derivative of f(x)=x^2sqrt(x-5x) is -(5x^2)/(sqrt(-x))
What is the first derivative of f(x)=x^2sqrt(x-5x) ?
The first derivative of f(x)=x^2sqrt(x-5x) is -(5x^2)/(sqrt(-x))