What is the derivative of e^{2x}(2x+3)^7 ?

The derivative of e^{2x}(2x+3)^7 is e^{2x}*2(2x+3)^7+14(2x+3)^6e^{2x}

What is the first derivative of e^{2x}(2x+3)^7 ?

The first derivative of e^{2x}(2x+3)^7 is e^{2x}*2(2x+3)^7+14(2x+3)^6e^{2x}

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derivative of

e^{2 x} (2 x + 3)^{7}

e^{2 x} \cdot 2 (2 x + 3)^{7} + 14 (2 x + 3)^{6} e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} (2 x + 3)^{7})

Apply the Product Rule:

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

f = e^{2 x}, g = (2 x + 3)^{7}

= \frac{d}{d x} (e^{2 x}) (2 x + 3)^{7} + \frac{d}{d x} ((2 x + 3)^{7}) e^{2 x}

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

\frac{d}{d x} ((2 x + 3)^{7}) = 14 (2 x + 3)^{6}

= e^{2 x} \cdot 2 (2 x + 3)^{7} + 14 (2 x + 3)^{6} e^{2 x}

What is the derivative of e^{2x}(2x+3)^7 ?
The derivative of e^{2x}(2x+3)^7 is e^{2x}*2(2x+3)^7+14(2x+3)^6e^{2x}
What is the first derivative of e^{2x}(2x+3)^7 ?
The first derivative of e^{2x}(2x+3)^7 is e^{2x}*2(2x+3)^7+14(2x+3)^6e^{2x}