What is the derivative of (1+w)sqrt(w^3+9) ?

The derivative of (1+w)sqrt(w^3+9) is (3w^2+5w^3+18)/(2sqrt(w^3+9))

What is the first derivative of (1+w)sqrt(w^3+9) ?

The first derivative of (1+w)sqrt(w^3+9) is (3w^2+5w^3+18)/(2sqrt(w^3+9))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(1 + w) w^{3} + 9

\frac{3 w ^{2} + 5 w ^{3} + 18}{2 w ^{3} + 9}

Solution steps

\frac{d}{d w} ((1 + w) w^{3} + 9)

Apply the Product Rule:

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

f = 1 + w, g = w^{3} + 9

= \frac{d}{d w} (1 + w) w^{3} + 9 + \frac{d}{d w} (w^{3} + 9) (1 + w)

\frac{d}{d w} (1 + w) = 1

\frac{d}{d w} (w^{3} + 9) = \frac{3 w ^{2}}{2 w ^{3} + 9}

= 1 \cdot w^{3} + 9 + \frac{3 w ^{2}}{2 w ^{3} + 9} (1 + w)

Simplify

1 \cdot w^{3} + 9 + \frac{3 w ^{2}}{2 w ^{3} + 9} (1 + w) : \frac{3 w ^{2} + 5 w ^{3} + 18}{2 w ^{3} + 9}

= \frac{3 w ^{2} + 5 w ^{3} + 18}{2 w ^{3} + 9}

y = \frac{5 x}{x}

\frac{d}{d x} (4 x^{\frac{1}{x}})

y^{^{''}} + y = 0.75 sin (t) - 0.25 sin (3 t)

\int 2 x + 4 d x

x = 2 y, x + 1 = (y - 1)^{2}

What is the derivative of (1+w)sqrt(w^3+9) ?
The derivative of (1+w)sqrt(w^3+9) is (3w^2+5w^3+18)/(2sqrt(w^3+9))
What is the first derivative of (1+w)sqrt(w^3+9) ?
The first derivative of (1+w)sqrt(w^3+9) is (3w^2+5w^3+18)/(2sqrt(w^3+9))