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Derivative of:
Derivative of x^2-7*x
Derivative of (sin(x))^2+(cos(x))^2
Derivative of sqrt(y)
Derivative of sin(2*t)
Identical expressions
(x^ two +7x- one)^ three
(x squared plus 7x minus 1) cubed
(x to the power of two plus 7x minus one) to the power of three
(x2+7x-1)3
x2+7x-13
(x²+7x-1)³
(x to the power of 2+7x-1) to the power of 3
x^2+7x-1^3
Similar expressions
(x^2+7x+1)^3
(x^2-7x-1)^3

The derivative of the function/ (x^2+7x-1)^3

Derivative of (x^2+7x-1)^3

The solution

You have entered [src]

              3
/ 2          \ 
\x  + 7*x - 1/

$$\left(x^{2} + 7 x - 1\right)^{3}$$

  /              3\
d |/ 2          \ |
--\\x  + 7*x - 1/ /
dx

$$\frac{d}{d x} \left(x^{2} + 7 x - 1\right)^{3}$$

Transform

Detail solution

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

$3 \cdot \left(2 x + 7\right) \left(x^{2} + 7 x - 1\right)^{2}$
Now simplify:

$\left(6 x + 21\right) \left(x^{2} + 7 x - 1\right)^{2}$

The answer is:

$\left(6 x + 21\right) \left(x^{2} + 7 x - 1\right)^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              2           
/ 2          \            
\x  + 7*x - 1/ *(21 + 6*x)

$$\left(6 x + 21\right) \left(x^{2} + 7 x - 1\right)^{2}$$

Simplify

The second derivative [src]

  /      2      \ /      2            2      \
6*\-1 + x  + 7*x/*\-1 + x  + (7 + 2*x)  + 7*x/

$$6 \left(x^{2} + 7 x - 1\right) \left(x^{2} + 7 x + \left(2 x + 7\right)^{2} - 1\right)$$

Simplify

The third derivative [src]

            /              2      2       \
6*(7 + 2*x)*\-6 + (7 + 2*x)  + 6*x  + 42*x/

$$6 \cdot \left(2 x + 7\right) \left(6 x^{2} + 42 x + \left(2 x + 7\right)^{2} - 6\right)$$

Simplify

The graph

Derivative of (x^2+7x-1)^3