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Derivative of:
Derivative of f(x)=x^3
Derivative of (-6)/x^4
Derivative of y=√4-x^2
Derivative of x^(x^2+1)
Identical expressions
e^(ten *(x- five))
e to the power of (10 multiply by (x minus 5))
e to the power of (ten multiply by (x minus five))
e(10*(x-5))
e10*x-5
e^(10(x-5))
e(10(x-5))
e10x-5
e^10x-5
Similar expressions
e^(10*(x+5))

The derivative of the function/ e^(10*(x-5))

Derivative of e^(10*(x-5))

The solution

You have entered [src]

 10*(x - 5)
E

$$e^{10 \left(x - 5\right)}$$

E^(10*(x - 5))

Detail solution

Let $u = 10 \left(x - 5\right)$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} 10 \left(x - 5\right)$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Differentiate $x - 5$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $-5$ is zero.
    The result is: $1$
  So, the result is: $10$
The result of the chain rule is:

$10 e^{10 x - 50}$

The answer is:

$10 e^{10 x - 50}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -50 + 10*x
10*e

$$10 e^{10 x - 50}$$

Simplify

The second derivative [src]

     -50 + 10*x
100*e

$$100 e^{10 x - 50}$$

Simplify

The third derivative [src]

      -50 + 10*x
1000*e

$$1000 e^{10 x - 50}$$

Simplify