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Popular >

derivative of (x^2-5x+1(2x+3))

Solution

\frac{d}{d x} ((x^{2} - 5 x + 1) (2 x + 3))

Solution

6 x^{2} - 14 x - 13

Solution steps

\frac{d}{d x} ((x^{2} - 5 x + 1) (2 x + 3))

Apply the Product Rule:

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

f = x^{2} - 5 x + 1, g = 2 x + 3

= \frac{d}{d x} (x^{2} - 5 x + 1) (2 x + 3) + \frac{d}{d x} (2 x + 3) (x^{2} - 5 x + 1)

\frac{d}{d x} (x^{2} - 5 x + 1) = 2 x - 5

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

= (2 x - 5) (2 x + 3) + 2 (x^{2} - 5 x + 1)

Simplify

(2 x - 5) (2 x + 3) + 2 (x^{2} - 5 x + 1) : 6 x^{2} - 14 x - 13

= 6 x^{2} - 14 x - 13

Popular Examples

(\partial)/(\partial y)(((ax+by))/(cx+dy))

\frac{\partial}{\partial y} (\frac{( a x + b y )}{c x + d y})

y^{''}=e^{(3t)}

y^{^{''}} = e^{(3 t)}

area-x^2+5x,x^2-3x area

- x^{2} + 5 x, x^{2} - 3 x

integral from 4 to 5 of x/(x^2+6x+13)

\int_{4}^{5} \frac{x}{x ^{2} + 6 x + 13} d x

(\partial)/(\partial x)(6x)

\frac{\partial}{\partial x} (6 x)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-5x+1(2x+3)) ?
The derivative of (x^2-5x+1(2x+3)) is 6x^2-14x-13
What is the first derivative of (x^2-5x+1(2x+3)) ?
The first derivative of (x^2-5x+1(2x+3)) is 6x^2-14x-13