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Derivative of:
Derivative of e^(7*x)
Derivative of x^-9
Derivative of y=7x+4
Derivative of x/(9-x^2)
Identical expressions
y=sec^ two *(3x)
y equally sec squared multiply by (3x)
y equally sec to the power of two multiply by (3x)
y=sec2*(3x)
y=sec2*3x
y=sec²*(3x)
y=sec to the power of 2*(3x)
y=sec^2(3x)
y=sec2(3x)
y=sec23x
y=sec^23x

The derivative of the function/ y=sec^2*(3x)

Derivative of y=sec^2*(3x)

The solution

You have entered [src]

   2     
sec (3*x)

$$\sec^{2}{\left(3 x \right)}$$

sec(3*x)^2

Detail solution

Let $u = \sec{\left(3 x \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sec{\left(3 x \right)}$ :
1. Rewrite the function to be differentiated:
  
  $\sec{\left(3 x \right)} = \frac{1}{\cos{\left(3 x \right)}}$
2. Let $u = \cos{\left(3 x \right)}$ .
3. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(3 x \right)}$ :
  1. Let $u = 3 x$ .
  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 $\frac{d}{d x} 3 x$ :
    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: $3$
    The result of the chain rule is:
    
    $- 3 \sin{\left(3 x \right)}$
  The result of the chain rule is:
  
  $\frac{3 \sin{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}}$
The result of the chain rule is:

$\frac{6 \sin{\left(3 x \right)} \sec{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}}$
Now simplify:

$\frac{6 \sin{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}}$

The answer is:

$\frac{6 \sin{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2              
6*sec (3*x)*tan(3*x)

$$6 \tan{\left(3 x \right)} \sec^{2}{\left(3 x \right)}$$

Simplify

The second derivative [src]

      2      /         2     \
18*sec (3*x)*\1 + 3*tan (3*x)/

$$18 \left(3 \tan^{2}{\left(3 x \right)} + 1\right) \sec^{2}{\left(3 x \right)}$$

Simplify

The third derivative [src]

       2      /         2     \         
216*sec (3*x)*\2 + 3*tan (3*x)/*tan(3*x)

$$216 \left(3 \tan^{2}{\left(3 x \right)} + 2\right) \tan{\left(3 x \right)} \sec^{2}{\left(3 x \right)}$$

Simplify

The graph

Derivative of y=sec^2*(3x)