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2^x*sin^2x

Derivative of 2^x*sin^2x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 x    2   
2 *sin (x)
$$2^{x} \sin^{2}{\left(x \right)}$$
d / x    2   \
--\2 *sin (x)/
dx            
$$\frac{d}{d x} 2^{x} \sin^{2}{\left(x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 x    2                x              
2 *sin (x)*log(2) + 2*2 *cos(x)*sin(x)
$$2^{x} \log{\left(2 \right)} \sin^{2}{\left(x \right)} + 2 \cdot 2^{x} \sin{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
 x /       2           2         2       2                            \
2 *\- 2*sin (x) + 2*cos (x) + log (2)*sin (x) + 4*cos(x)*log(2)*sin(x)/
$$2^{x} \left(- 2 \sin^{2}{\left(x \right)} + \log{\left(2 \right)}^{2} \sin^{2}{\left(x \right)} + 4 \log{\left(2 \right)} \sin{\left(x \right)} \cos{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right)$$
The third derivative [src]
 x /   3       2                          /   2         2   \               2                 \
2 *\log (2)*sin (x) - 8*cos(x)*sin(x) - 6*\sin (x) - cos (x)/*log(2) + 6*log (2)*cos(x)*sin(x)/
$$2^{x} \left(\log{\left(2 \right)}^{3} \sin^{2}{\left(x \right)} - 8 \sin{\left(x \right)} \cos{\left(x \right)} + 6 \log{\left(2 \right)}^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 6 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)}\right)$$
The graph
Derivative of 2^x*sin^2x