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Popular >

derivative of e^x(x-1)

Solution

derivative of

e^{x} (x - 1)

Solution

e^{x} x

Solution steps

\frac{d}{d x} (e^{x} (x - 1))

Apply the Product Rule:

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

f = e^{x}, g = x - 1

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

\frac{d}{d x} (e^{x}) = e^{x}

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

= e^{x} (x - 1) + 1 \cdot e^{x}

Simplify

e^{x} (x - 1) + 1 \cdot e^{x} : e^{x} x

= e^{x} x

Popular Examples

y^'+sin(t)y=sin(t),y(0)=6

y^{^{'}} + sin (t) y = sin (t), y (0) = 6

(\partial)/(\partial x)((x^2-2x)cos(y))

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

derivative of (e^{3x}(cos(2x)))

\frac{d}{d x} ((e^{3 x}) (cos (2 x)))

16 y^{''} + 8 y^{'} + y = 0

limit as x approaches 0 of (tan(4x)cos(6x)-tan(4x))/(24x^3)

x \to 0 lim (\frac{tan ( 4 x ) cos ( 6 x ) - tan ( 4 x )}{24 x ^{3}})

Frequently Asked Questions (FAQ)

What is the derivative of e^x(x-1) ?
The derivative of e^x(x-1) is e^xx
What is the first derivative of e^x(x-1) ?
The first derivative of e^x(x-1) is e^xx