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

The derivative of e^{3x}(x^2+y^2) is e^{3x}*3(x^2+y^2)+(2x+2y(dy)/(dx))e^{3x}

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

The first derivative of e^{3x}(x^2+y^2) is e^{3x}*3(x^2+y^2)+(2x+2y(dy)/(dx))e^{3x}

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

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

Solution steps

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

Apply the Product Rule:

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

f = e^{3 x}, g = x^{2} + y^{2}

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (x^{2} + y^{2}) = 2 x + 2 y \frac{d y}{d x}

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

What is the derivative of e^{3x}(x^2+y^2) ?
The derivative of e^{3x}(x^2+y^2) is e^{3x}*3(x^2+y^2)+(2x+2y(dy)/(dx))e^{3x}
What is the first derivative of e^{3x}(x^2+y^2) ?
The first derivative of e^{3x}(x^2+y^2) is e^{3x}*3(x^2+y^2)+(2x+2y(dy)/(dx))e^{3x}