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Popular >

derivative of f(x)=(x+2)sqrt(2x-3)

Solution

derivative of

f (x) = (x + 2) 2 x - 3

Solution

\frac{3 x - 1}{2 x - 3}

Solution steps

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

Apply the Product Rule:

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

f = x + 2, g = 2 x - 3

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

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

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

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

Simplify

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

= \frac{3 x - 1}{2 x - 3}

Popular Examples

(\partial)/(\partial y)(((x+y))/((y+z)))

\frac{\partial}{\partial y} (\frac{( x + y )}{( y + z )})

(\partial)/(\partial x)(x/(x^6-y^3))

\frac{\partial}{\partial x} (\frac{x}{x ^{6} - y ^{3}})

(dy)/(dx)=4x+y,y(0)=9

\frac{d y}{d x} = 4 x + y, y (0) = 9

derivative of x^{16}

\frac{d}{d x} (x^{16})

y^{''}-2y^'=sin(x)

y^{^{''}} - 2 y^{^{'}} = sin (x)

Frequently Asked Questions (FAQ)

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