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

The derivative of f(x)=xsin(2^x) is sin(2^x)+ln(2)*2^xxcos(2^x)

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

The first derivative of f(x)=xsin(2^x) is sin(2^x)+ln(2)*2^xxcos(2^x)

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (2^{x}) + cos (2^{x}) \cdot 2^{x} ln (2) x

Simplify

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

\frac{1}{x} e^{y} tan (y) y^{^{'}} = e^{x + y}

\frac{\partial}{\partial y} (\frac{4 x}{x ^{2} + y ^{2}})

\int \frac{1}{2} (cos (x))^{2} d x

f (x) = \frac{40}{x}, (1, 40)

\int (\frac{x + 1}{x}) d x

What is the derivative of f(x)=xsin(2^x) ?
The derivative of f(x)=xsin(2^x) is sin(2^x)+ln(2)*2^xxcos(2^x)
What is the first derivative of f(x)=xsin(2^x) ?
The first derivative of f(x)=xsin(2^x) is sin(2^x)+ln(2)*2^xxcos(2^x)