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Derivative of:
Derivative of x^12
Derivative of -e^x
Derivative of sin(2*x^2+3)
Derivative of f(x)=7
Identical expressions
y=✓x^ two -7x+ fifteen
y equally ✓x squared minus 7x plus 15
y equally ✓x to the power of two minus 7x plus fifteen
y=✓x2-7x+15
y=✓x²-7x+15
y=✓x to the power of 2-7x+15
Similar expressions
y=✓x^2+7x+15
y=✓x^2-7x-15

The derivative of the function/ y=✓x^2-7x+15

Derivative of y=✓x^2-7x+15

The solution

You have entered [src]

     2           
  ___            
\/ x   - 7*x + 15

$$\left(\sqrt{x}\right)^{2} - 7 x + 15$$

  /     2           \
d |  ___            |
--\\/ x   - 7*x + 15/
dx

$$\frac{d}{d x} \left(\left(\sqrt{x}\right)^{2} - 7 x + 15\right)$$

Transform

Detail solution

Differentiate $\left(\sqrt{x}\right)^{2} - 7 x + 15$ term by term:
1. Let $u = \sqrt{x}$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  The result of the chain rule is:
  
  $1$
4. The derivative of a constant times a function is the constant times the derivative of the function.
  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: $7$
  So, the result is: $-7$
5. The derivative of the constant $15$ is zero.
The result is: $-6$

The answer is:

$-6$

The first derivative [src]

     x
-7 + -
     x

$$-7 + \frac{x}{x}$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify