What is the derivative of (1+4x^{3/2}) ?

The derivative of (1+4x^{3/2}) is 6(4x+1)^{1/2}

What is the first derivative of (1+4x^{3/2}) ?

The first derivative of (1+4x^{3/2}) is 6(4x+1)^{1/2}

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\frac{d}{d x} ((1 + 4 x)^{\frac{3}{2}})

6 (4 x + 1)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((1 + 4 x)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (1 + 4 x)

= \frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (1 + 4 x)

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

= \frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \cdot 4

Simplify

\frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (4 x + 1)^{\frac{1}{2}}

= 6 (4 x + 1)^{\frac{1}{2}}

\int_{0}^{\infty} 2 e^{- 2 x} d x

\frac{d y}{d x}, y = 7 x^{8}

\int 3 x - 4 x d x

x \to 3 - lim (\frac{2 x}{x - 3})

What is the derivative of (1+4x^{3/2}) ?
The derivative of (1+4x^{3/2}) is 6(4x+1)^{1/2}
What is the first derivative of (1+4x^{3/2}) ?
The first derivative of (1+4x^{3/2}) is 6(4x+1)^{1/2}