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Derivative of:
Derivative of log(x^2+5)
Derivative of e^(-2*x)
Derivative of sin(x)-x*cos(x)
Derivative of e^x*x
Identical expressions
x^ two *cos(one)/x
x squared multiply by co sinus of e of (1) divide by x
x to the power of two multiply by co sinus of e of (one) divide by x
x2*cos(1)/x
x2*cos1/x
x²*cos(1)/x
x to the power of 2*cos(1)/x
x^2cos(1)/x
x2cos(1)/x
x2cos1/x
x^2cos1/x
x^2*cos(1) divide by x

The derivative of the function/ x^2*cos(1)/x

Derivative of x^2*cos(1)/x

The solution

You have entered [src]

 2       
x *cos(1)
---------
    x

$$\frac{x^{2} \cos{\left(1 \right)}}{x}$$

(x^2*cos(1))/x

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2} \cos{\left(1 \right)}$ and $g{\left(x \right)} = x$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $2 x \cos{\left(1 \right)}$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
Now plug in to the quotient rule:

$\cos{\left(1 \right)}$

The answer is:

$\cos{\left(1 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

cos(1)

$$\cos{\left(1 \right)}$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify