What is the derivative of 5sqrt(x)(x^3-5sqrt(x)+5) ?

The derivative of 5sqrt(x)(x^3-5sqrt(x)+5) is 5(-5/2+(7x^3-5sqrt(x)+5)/(2sqrt(x)))

What is the first derivative of 5sqrt(x)(x^3-5sqrt(x)+5) ?

The first derivative of 5sqrt(x)(x^3-5sqrt(x)+5) is 5(-5/2+(7x^3-5sqrt(x)+5)/(2sqrt(x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

5 x (x^{3} - 5 x + 5)

5 (- \frac{5}{2} + \frac{7 x ^{3} - 5 x + 5}{2 x})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = x^{3} - 5 x + 5

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

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

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

= 5 (\frac{1}{2 x} (x^{3} - 5 x + 5) + (3 x^{2} - \frac{5}{2 x}) x)

Simplify

5 (\frac{1}{2 x} (x^{3} - 5 x + 5) + (3 x^{2} - \frac{5}{2 x}) x) : 5 (- \frac{5}{2} + \frac{7 x ^{3} - 5 x + 5}{2 x})

= 5 (- \frac{5}{2} + \frac{7 x ^{3} - 5 x + 5}{2 x})

\frac{\partial}{\partial x} (4 ln (\frac{2 x y}{7 z}))

h (w) = \frac{4 w ^{5} - w}{w}

\int x e^{1 - x} d x

f (x) = x sin (\frac{1}{x})

y = x^{2} - 3 x - 2, (2, - 4)

What is the derivative of 5sqrt(x)(x^3-5sqrt(x)+5) ?
The derivative of 5sqrt(x)(x^3-5sqrt(x)+5) is 5(-5/2+(7x^3-5sqrt(x)+5)/(2sqrt(x)))
What is the first derivative of 5sqrt(x)(x^3-5sqrt(x)+5) ?
The first derivative of 5sqrt(x)(x^3-5sqrt(x)+5) is 5(-5/2+(7x^3-5sqrt(x)+5)/(2sqrt(x)))