What is the derivative of-3xsqrt(x+1) ?

The derivative of-3xsqrt(x+1) is -(3(3x+2))/(2sqrt(x+1))

What is the first derivative of-3xsqrt(x+1) ?

The first derivative of-3xsqrt(x+1) is -(3(3x+2))/(2sqrt(x+1))

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derivative of

- 3 x x + 1

- \frac{3 ( 3 x + 2 )}{2 x + 1}

Solution steps

\frac{d}{d x} (- 3 x x + 1)

Take the constant out:

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

= - 3 \frac{d}{d x} (x x + 1)

Apply the Product Rule:

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

f = x, g = x + 1

= - 3 (\frac{d x}{d x} x + 1 + \frac{d}{d x} (x + 1) x)

\frac{d x}{d x} = 1

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

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

Simplify

- 3 (1 \cdot x + 1 + \frac{1}{2 x + 1} x) : - \frac{3 ( 3 x + 2 )}{2 x + 1}

= - \frac{3 ( 3 x + 2 )}{2 x + 1}

What is the derivative of-3xsqrt(x+1) ?
The derivative of-3xsqrt(x+1) is -(3(3x+2))/(2sqrt(x+1))
What is the first derivative of-3xsqrt(x+1) ?
The first derivative of-3xsqrt(x+1) is -(3(3x+2))/(2sqrt(x+1))