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Popular >

derivative of Xsqrt(X+1)

Solution

derivative of

X X + 1

Solution

\frac{3 X + 2}{2 X + 1}

Solution steps

\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

= \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}

= 1 \cdot X + 1 + \frac{1}{2 X + 1} X

Simplify

1 \cdot X + 1 + \frac{1}{2 X + 1} X : \frac{3 X + 2}{2 X + 1}

= \frac{3 X + 2}{2 X + 1}

Popular Examples

integral of (t-3)/(sqrt(t))

\int \frac{t - 3}{t} d t

(\partial)/(\partial x)(ysqrt(x)-y^2-x+3y)

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

derivative of (9sqrt(x+8))x^2 derivative of

(9 x + 8) x^{2}

integral from 0 to infinity of (ye^{(-y)/a})/(a)

\int_{0}^{\infty} \frac{y e ^{\frac{- y}{a}}}{a} d y

y^{''}-2y^'+y=2e^x

y^{^{''}} - 2 y^{^{'}} + y = 2 e^{x}

Frequently Asked Questions (FAQ)

What is the derivative of Xsqrt(X+1) ?
The derivative of Xsqrt(X+1) is (3X+2)/(2sqrt(X+1))
What is the first derivative of Xsqrt(X+1) ?
The first derivative of Xsqrt(X+1) is (3X+2)/(2sqrt(X+1))