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Popular >

derivative of-e^x(x+6)

Solution

\frac{d}{d x} (- e^{x} (x + 6))

Solution

- e^{x} x - 7 e^{x}

Solution steps

\frac{d}{d x} (- e^{x} (x + 6))

Take the constant out:

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

= - \frac{d}{d x} (e^{x} (x + 6))

Apply the Product Rule:

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

f = e^{x}, g = x + 6

= - (\frac{d}{d x} (e^{x}) (x + 6) + \frac{d}{d x} (x + 6) e^{x})

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

\frac{d}{d x} (x + 6) = 1

= - (e^{x} (x + 6) + 1 \cdot e^{x})

Simplify

- (e^{x} (x + 6) + 1 \cdot e^{x}) : - e^{x} x - 7 e^{x}

= - e^{x} x - 7 e^{x}

Popular Examples

limit as x approaches 3+of (4-x)/(9-x^2)

x \to 3 + lim (\frac{4 - x}{9 - x ^{2}})

integral of (sin(3x))/(3+3cos(3x))

\int \frac{sin ( 3 x )}{3 + 3 cos ( 3 x )} d x

implicit (dy)/(dx),3xy=6 implicit derivative

\frac{d y}{d x}, 3 x y = 6

integral from-1 to 2 of (x^3)

\int_{- 1}^{2} (x^{3}) d x

area f(x)=2x+1,1,5 area

f (x) = 2 x + 1, 1, 5

Frequently Asked Questions (FAQ)

What is the derivative of-e^x(x+6) ?
The derivative of-e^x(x+6) is -e^xx-7e^x
What is the first derivative of-e^x(x+6) ?
The first derivative of-e^x(x+6) is -e^xx-7e^x