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Derivative of:
Derivative of e^cos(x)
Derivative of ln(x+3)^3
Derivative of cos(3*x)^(2)
Derivative of -cos(2*x)
Identical expressions
x^ three - three ^x
x cubed minus 3 to the power of x
x to the power of three minus three to the power of x
x3-3x
x³-3^x
x to the power of 3-3 to the power of x
Similar expressions
x^3+3^x

The derivative of the function/ x^3-3^x

Derivative of x^3-3^x

The solution

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 3    x
x  - 3

$$- 3^{x} + x^{3}$$

d / 3    x\
--\x  - 3 /
dx

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

Transform

Detail solution

Differentiate $- 3^{x} + x^{3}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. $\frac{d}{d x} 3^{x} = 3^{x} \log{\left(3 \right)}$
  So, the result is: $- 3^{x} \log{\left(3 \right)}$
The result is: $- 3^{x} \log{\left(3 \right)} + 3 x^{2}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2    x       
3*x  - 3 *log(3)

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

Simplify

The second derivative [src]

       x    2   
6*x - 3 *log (3)

$$- 3^{x} \log{\left(3 \right)}^{2} + 6 x$$

Simplify

The third derivative [src]

     x    3   
6 - 3 *log (3)

$$- 3^{x} \log{\left(3 \right)}^{3} + 6$$

Simplify

The graph

Derivative of x^3-3^x