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

The derivative of 2^{xsin(x}) is ln(2)*2^{xsin(x)}(sin(x)+xcos(x))

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

The first derivative of 2^{xsin(x}) is ln(2)*2^{xsin(x)}(sin(x)+xcos(x))

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\frac{d}{d x} (2^{x s i n (x)})

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

Solution steps

\frac{d}{d x} (2^{x s i n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{x s i n (x)} = e^{x s i n (x) l n (2)}

= \frac{d}{d x} (e^{x s i n (x) l n (2)})

Apply the chain rule:

e^{x s i n (x) l n (2)} \frac{d}{d x} (x sin (x) ln (2))

= e^{x s i n (x) l n (2)} \frac{d}{d x} (x sin (x) ln (2))

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

= e^{x s i n (x) l n (2)} ln (2) (sin (x) + x cos (x))

e^{x s i n (x) l n (2)} = 2^{x s i n (x)}

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

f (x) = 5 tan (x)

\frac{d}{d x} (e cos (x))

\int e^{t} cos (e^{t}) d t

f (x) = - 5

y^{^{'}} = (x - 5) e^{- 2 y}, y (5) = ln (5)

What is the derivative of 2^{xsin(x}) ?
The derivative of 2^{xsin(x}) is ln(2)*2^{xsin(x)}(sin(x)+xcos(x))
What is the first derivative of 2^{xsin(x}) ?
The first derivative of 2^{xsin(x}) is ln(2)*2^{xsin(x)}(sin(x)+xcos(x))