What is the derivative of e^{2x}*sin(x^2+5) ?

The derivative of e^{2x}*sin(x^2+5) is e^{2x}*2sin(x^2+5)+cos(x^2+5)*2xe^{2x}

What is the first derivative of e^{2x}*sin(x^2+5) ?

The first derivative of e^{2x}*sin(x^2+5) is e^{2x}*2sin(x^2+5)+cos(x^2+5)*2xe^{2x}

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\frac{d}{d x} (e^{2 x} \cdot sin (x^{2} + 5))

e^{2 x} \cdot 2 sin (x^{2} + 5) + cos (x^{2} + 5) \cdot 2 x e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} sin (x^{2} + 5))

Apply the Product Rule:

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

f = e^{2 x}, g = sin (x^{2} + 5)

= \frac{d}{d x} (e^{2 x}) sin (x^{2} + 5) + \frac{d}{d x} (sin (x^{2} + 5)) e^{2 x}

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

\frac{d}{d x} (sin (x^{2} + 5)) = cos (x^{2} + 5) \cdot 2 x

= e^{2 x} \cdot 2 sin (x^{2} + 5) + cos (x^{2} + 5) \cdot 2 x e^{2 x}

2 x^{3} - x^{2} + 3

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

\frac{d y}{d x} = (x + y + 9)^{2}

\int_{- 2}^{3} \frac{25}{x ^{4}} d x

What is the derivative of e^{2x}*sin(x^2+5) ?
The derivative of e^{2x}*sin(x^2+5) is e^{2x}*2sin(x^2+5)+cos(x^2+5)*2xe^{2x}
What is the first derivative of e^{2x}*sin(x^2+5) ?
The first derivative of e^{2x}*sin(x^2+5) is e^{2x}*2sin(x^2+5)+cos(x^2+5)*2xe^{2x}