What is the derivative of 2x^3sqrt(25-x^2) ?

The derivative of 2x^3sqrt(25-x^2) is (2(-4x^4+75x^2))/(sqrt(25-x^2))

What is the first derivative of 2x^3sqrt(25-x^2) ?

The first derivative of 2x^3sqrt(25-x^2) is (2(-4x^4+75x^2))/(sqrt(25-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

2 x^{3} 25 - x^{2}

\frac{2 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (2 x^{3} 25 - x^{2})

Take the constant out:

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

= 2 \frac{d}{d x} (x^{3} 25 - x^{2})

Apply the Product Rule:

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

f = x^{3}, g = 25 - x^{2}

= 2 (\frac{d}{d x} (x^{3}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{3})

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

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 2 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3})

Simplify

2 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3}) : \frac{2 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

= \frac{2 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

x \to 0 + lim (1)

x \to 1 lim (\frac{e ^{x}}{x - 1})

\int 15 arctan (x) d x

\frac{d}{d x} (- x^{2} + 4 x)

y = x (x - 10)

What is the derivative of 2x^3sqrt(25-x^2) ?
The derivative of 2x^3sqrt(25-x^2) is (2(-4x^4+75x^2))/(sqrt(25-x^2))
What is the first derivative of 2x^3sqrt(25-x^2) ?
The first derivative of 2x^3sqrt(25-x^2) is (2(-4x^4+75x^2))/(sqrt(25-x^2))