What is the derivative of e^{3*x}*(2*sin(4*x)) ?

The derivative of e^{3*x}*(2*sin(4*x)) is 2(e^{3x}*3sin(4x)+cos(4x)*4e^{3x})

What is the first derivative of e^{3*x}*(2*sin(4*x)) ?

The first derivative of e^{3*x}*(2*sin(4*x)) is 2(e^{3x}*3sin(4x)+cos(4x)*4e^{3x})

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derivative of

e^{3 \cdot x} \cdot (2 \cdot sin (4 \cdot x))

2 (e^{3 x} \cdot 3 sin (4 x) + cos (4 x) \cdot 4 e^{3 x})

Solution steps

\frac{d}{d x} (e^{3 x} \cdot 2 sin (4 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (e^{3 x} sin (4 x))

Apply the Product Rule:

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

f = e^{3 x}, g = sin (4 x)

= 2 (\frac{d}{d x} (e^{3 x}) sin (4 x) + \frac{d}{d x} (sin (4 x)) e^{3 x})

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

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

= 2 (e^{3 x} \cdot 3 sin (4 x) + cos (4 x) \cdot 4 e^{3 x})

\int \frac{1}{( 2 y + 5 ) ^{2}} d y

n = 1 \sum \infty (\frac{2}{3})^{n}

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

\int_{- 1}^{2} 1 + x^{2} d x

\frac{d}{d x} (cos (x) + x sin (x))

What is the derivative of e^{3*x}*(2*sin(4*x)) ?
The derivative of e^{3*x}*(2*sin(4*x)) is 2(e^{3x}*3sin(4x)+cos(4x)*4e^{3x})
What is the first derivative of e^{3*x}*(2*sin(4*x)) ?
The first derivative of e^{3*x}*(2*sin(4*x)) is 2(e^{3x}*3sin(4x)+cos(4x)*4e^{3x})