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y=log(2)*sin^2x

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Identical expressions
y=log(two)*sin^2x
y equally logarithm of (2) multiply by sinus of squared x
y equally logarithm of (two) multiply by sinus of squared x
y=log(2)*sin2x
y=log2*sin2x
y=log(2)*sin²x
y=log(2)*sin to the power of 2x
y=log(2)sin^2x
y=log(2)sin2x
y=log2sin2x
y=log2sin^2x

The derivative of the function/ y=log(2)*sin^2x

Derivative of y=log(2)*sin^2x

The solution

You have entered [src]

          2   
log(2)*sin (x)

$$\log{\left(2 \right)} \sin^{2}{\left(x \right)}$$

d /          2   \
--\log(2)*sin (x)/
dx

$$\frac{d}{d x} \log{\left(2 \right)} \sin^{2}{\left(x \right)}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sin{\left(x \right)}$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  The result of the chain rule is:
  
  $2 \sin{\left(x \right)} \cos{\left(x \right)}$
So, the result is: $2 \log{\left(2 \right)} \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

$\log{\left(2 \right)} \sin{\left(2 x \right)}$

The answer is:

$\log{\left(2 \right)} \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*cos(x)*log(2)*sin(x)

$$2 \log{\left(2 \right)} \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

   /   2         2   \       
-2*\sin (x) - cos (x)/*log(2)

$$- 2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)}$$

Simplify

The third derivative [src]

-8*cos(x)*log(2)*sin(x)

$$- 8 \log{\left(2 \right)} \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph

Derivative of y=log(2)*sin^2x