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Popular >

derivative of (Ax+Be^x)

Solution

\frac{d}{d x} ((A x + B) e^{x})

Solution

A e^{x} + e^{x} (A x + B)

Solution steps

\frac{d}{d x} ((A x + B) e^{x})

Treat

A, B

as constants

Apply the Product Rule:

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

f = A x + B, g = e^{x}

= \frac{d}{d x} (A x + B) e^{x} + \frac{d}{d x} (e^{x}) (A x + B)

\frac{d}{d x} (A x + B) = A

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

= A e^{x} + e^{x} (A x + B)

Popular Examples

y^'+y=e^{9t},y(0)=-1

y^{^{'}} + y = e^{9 t}, y (0) = - 1

limit as x approaches 2 of (x+3)/(x+2)

x \to 2 lim (\frac{x + 3}{x + 2})

(\partial)/(\partial y)(xy^3+4ye^x-2y^2)

\frac{\partial}{\partial y} (x y^{3} + 4 y e^{x} - 2 y^{2})

(\partial)/(\partial y)(ln((y/x)^2))

\frac{\partial}{\partial y} (ln ((\frac{y}{x})^{2}))

tangent of f(x)=-3x^3-2x^2-x+3,\at x=-1 tangent of

f (x) = - 3 x^{3} - 2 x^{2} - x + 3, at x = - 1

Frequently Asked Questions (FAQ)

What is the derivative of (Ax+Be^x) ?
The derivative of (Ax+Be^x) is Ae^x+e^x(Ax+B)
What is the first derivative of (Ax+Be^x) ?
The first derivative of (Ax+Be^x) is Ae^x+e^x(Ax+B)