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Popular >

derivative of (Ax+Be^{2x})

Solution

\frac{d}{d x} ((A x + B) e^{2 x})

Solution

A e^{2 x} + e^{2 x} \cdot 2 (A x + B)

Solution steps

\frac{d}{d x} ((A x + B) e^{2 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^{2 x}

= \frac{d}{d x} (A x + B) e^{2 x} + \frac{d}{d x} (e^{2 x}) (A x + B)

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= A e^{2 x} + e^{2 x} \cdot 2 (A x + B)

Popular Examples

limit as x approaches 3 of 5x^2-7x-3

x \to 3 lim (5 x^{2} - 7 x - 3)

derivative of (10x^2-20x+20)e^{-6x}derivative of

(10 x^{2} - 20 x + 20) e^{- 6 x}

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

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

derivative of 4x^3+3x

\frac{d}{d x} (4 x^{3} + 3 x)

integral from-1 to 7 of (2x+7)-(x^2-4x)

\int_{- 1}^{7} (2 x + 7) - (x^{2} - 4 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (Ax+Be^{2x}) ?
The derivative of (Ax+Be^{2x}) is Ae^{2x}+e^{2x}*2(Ax+B)
What is the first derivative of (Ax+Be^{2x}) ?
The first derivative of (Ax+Be^{2x}) is Ae^{2x}+e^{2x}*2(Ax+B)