What is the derivative of 2^xsin(x) ?

The derivative of 2^xsin(x) is 2^xln(2)sin(x)+cos(x)*2^x

What is the first derivative of 2^xsin(x) ?

The first derivative of 2^xsin(x) is 2^xln(2)sin(x)+cos(x)*2^x

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\frac{d}{d x} (2^{x} sin (x))

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

Solution steps

\frac{d}{d x} (2^{x} sin (x))

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

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

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

\int cos (b + a x) d x

2 x^{2} y y^{^{'}} + 2 x y^{2} + 1 = 0

\int (4^{x}) d x

\frac{d}{d x} (3 ln (x + 1))

\frac{d}{d x} (35 x ln (13 x))

What is the derivative of 2^xsin(x) ?
The derivative of 2^xsin(x) is 2^xln(2)sin(x)+cos(x)*2^x
What is the first derivative of 2^xsin(x) ?
The first derivative of 2^xsin(x) is 2^xln(2)sin(x)+cos(x)*2^x