What is the derivative of 4x^4sqrt(25-x^2) ?

The derivative of 4x^4sqrt(25-x^2) is (4(-5x^5+100x^3))/(sqrt(25-x^2))

What is the first derivative of 4x^4sqrt(25-x^2) ?

The first derivative of 4x^4sqrt(25-x^2) is (4(-5x^5+100x^3))/(sqrt(25-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{4 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = 25 - x^{2}

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

Simplify

4 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4}) : \frac{4 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

= \frac{4 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

\frac{\partial}{\partial x} (4 x^{2} y + 6 x y^{2})

\frac{d}{d x} (\frac{7 x}{x ^{2} + 4})

\frac{1}{6} x^{3} + \frac{1}{2 x}

\frac{d}{d x} (4 + 3 f (x))

x \to 0 + lim (ln (\frac{9}{x ^{3}}))

What is the derivative of 4x^4sqrt(25-x^2) ?
The derivative of 4x^4sqrt(25-x^2) is (4(-5x^5+100x^3))/(sqrt(25-x^2))
What is the first derivative of 4x^4sqrt(25-x^2) ?
The first derivative of 4x^4sqrt(25-x^2) is (4(-5x^5+100x^3))/(sqrt(25-x^2))