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Derivative of:
Derivative of x^12
Derivative of -e^x
Derivative of (1+x)/(4-x^2)
Derivative of (1+sqrt(x))/(1-sqrt(x))
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=5cos(one -5x)
f(x) equally 5 co sinus of e of (1 minus 5x)
f(x) equally 5 co sinus of e of (one minus 5x)
fx=5cos1-5x
Similar expressions
f(x)=5cos(1+5x)

The derivative of the function/ f(x)=5cos(1-5x)

Derivative of f(x)=5cos(1-5x)

The solution

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5*cos(1 - 5*x)

$$5 \cos{\left(1 - 5 x \right)}$$

5*cos(1 - 5*x)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 1 - 5 x$ .
2. The derivative of cosine is negative sine:
  
  $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - 5 x\right)$ :
  1. Differentiate $1 - 5 x$ term by term:
    1. The derivative of the constant $1$ is zero.
    2. 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: $-5$
    The result is: $-5$
  The result of the chain rule is:
  
  $- 5 \sin{\left(5 x - 1 \right)}$
So, the result is: $- 25 \sin{\left(5 x - 1 \right)}$

The answer is:

$- 25 \sin{\left(5 x - 1 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-25*sin(-1 + 5*x)

$$- 25 \sin{\left(5 x - 1 \right)}$$

Simplify

The second derivative [src]

-125*cos(-1 + 5*x)

$$- 125 \cos{\left(5 x - 1 \right)}$$

Simplify

The third derivative [src]

625*sin(-1 + 5*x)

$$625 \sin{\left(5 x - 1 \right)}$$

Simplify