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Popular >

derivative of-e^x(x-7)

Solution

\frac{d}{d x} (- e^{x} (x - 7))

Solution

- e^{x} x + 6 e^{x}

Solution steps

\frac{d}{d x} (- e^{x} (x - 7))

Take the constant out:

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

= - \frac{d}{d x} (e^{x} (x - 7))

Apply the Product Rule:

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

f = e^{x}, g = x - 7

= - (\frac{d}{d x} (e^{x}) (x - 7) + \frac{d}{d x} (x - 7) e^{x})

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

\frac{d}{d x} (x - 7) = 1

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

Simplify

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

= - e^{x} x + 6 e^{x}

Popular Examples

(\partial)/(\partial y)(-10ysin(xy))

\frac{\partial}{\partial y} (- 10 y sin (x y))

derivative of y=x^{x^2}derivative of

y = x^{x^{2}}

(\partial)/(\partial x)(-xcos(y))

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

integral of 3cos(x)-1/(sqrt(x))

\int 3 cos (x) - \frac{1}{x} d x

integral from 1 to 11 of 1/(x-8)

\int_{1}^{11} \frac{1}{x - 8} d x

Frequently Asked Questions (FAQ)

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