Derivative of sin(7*x)

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sin(7*x)

\sin{\left(7 x \right)}

sin(7*x)

Detail solution

Let $u = 7 x$ .
The derivative of sine is cosine:

$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} 7 x$ :
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: $7$
The result of the chain rule is:

$7 \cos{\left(7 x \right)}$

The answer is:

7 \cos{\left(7 x \right)}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

7*cos(7*x)

7 \cos{\left(7 x \right)}

Simplify

The second derivative [src]

-49*sin(7*x)

- 49 \sin{\left(7 x \right)}

Simplify

The third derivative [src]

-343*cos(7*x)

- 343 \cos{\left(7 x \right)}

Simplify

The graph