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The derivative of the function/ y=log(6)sin4x

Derivative of y=log(6)sin4x

The solution

You have entered [src]

log(6)*sin(4*x)

$$\log{\left(6 \right)} \sin{\left(4 x \right)}$$

log(6)*sin(4*x)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 4 x$ .
2. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 4 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $4$
  The result of the chain rule is:
  
  $4 \cos{\left(4 x \right)}$
So, the result is: $4 \log{\left(6 \right)} \cos{\left(4 x \right)}$

The answer is:

$4 \log{\left(6 \right)} \cos{\left(4 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4*cos(4*x)*log(6)

$$4 \log{\left(6 \right)} \cos{\left(4 x \right)}$$

Simplify

The second derivative [src]

-16*log(6)*sin(4*x)

$$- 16 \log{\left(6 \right)} \sin{\left(4 x \right)}$$

Simplify

The third derivative [src]

-64*cos(4*x)*log(6)

$$- 64 \log{\left(6 \right)} \cos{\left(4 x \right)}$$

Simplify

The graph

Derivative of y=log(6)sin4x