What is the derivative of f(x)=(4x-1)x^{9/2} ?

The derivative of f(x)=(4x-1)x^{9/2} is (44x^{9/2}-9x^{7/2})/2

What is the first derivative of f(x)=(4x-1)x^{9/2} ?

The first derivative of f(x)=(4x-1)x^{9/2} is (44x^{9/2}-9x^{7/2})/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (4 x - 1) x^{\frac{9}{2}}

\frac{44 x ^{\frac{9}{2}} - 9 x ^{\frac{7}{2}}}{2}

Solution steps

\frac{d}{d x} ((4 x - 1) x^{\frac{9}{2}})

Apply the Product Rule:

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

f = 4 x - 1, g = x^{\frac{9}{2}}

= \frac{d}{d x} (4 x - 1) x^{\frac{9}{2}} + \frac{d}{d x} (x^{\frac{9}{2}}) (4 x - 1)

\frac{d}{d x} (4 x - 1) = 4

\frac{d}{d x} (x^{\frac{9}{2}}) = \frac{9 x ^{\frac{7}{2}}}{2}

= 4 x^{\frac{9}{2}} + \frac{9 x ^{\frac{7}{2}}}{2} (4 x - 1)

Simplify

4 x^{\frac{9}{2}} + \frac{9 x ^{\frac{7}{2}}}{2} (4 x - 1) : \frac{44 x ^{\frac{9}{2}} - 9 x ^{\frac{7}{2}}}{2}

= \frac{44 x ^{\frac{9}{2}} - 9 x ^{\frac{7}{2}}}{2}

x \to 0 lim ((x + 2)^{3})

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

\int \frac{1}{30} x d x

\frac{5}{2 ( s - 1 ) ^{2} + 8}

t \to 2 lim (ln (t))

What is the derivative of f(x)=(4x-1)x^{9/2} ?
The derivative of f(x)=(4x-1)x^{9/2} is (44x^{9/2}-9x^{7/2})/2
What is the first derivative of f(x)=(4x-1)x^{9/2} ?
The first derivative of f(x)=(4x-1)x^{9/2} is (44x^{9/2}-9x^{7/2})/2