Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^2*x
Derivative of x^sin(x)
Derivative of sqrt(x^2+1)
Derivative of 4/x^2
Identical expressions
log(two)(ax-b)+c^x+d
logarithm of (2)(ax minus b) plus c to the power of x plus d
logarithm of (two)(ax minus b) plus c to the power of x plus d
log(2)(ax-b)+cx+d
log2ax-b+cx+d
log2ax-b+c^x+d
Similar expressions
log(2)(ax-b)-c^x+d
log(2)(ax-b)+c^x-d
log(2)(ax+b)+c^x+d

The derivative of the function/ log(2)(ax-b)+c^x+d

Derivative of log(2)(ax-b)+c^x+d

The solution

You have entered [src]

                    x    
log(2)*(a*x - b) + c  + d

$$d + \left(c^{x} + \left(a x - b\right) \log{\left(2 \right)}\right)$$

log(2)*(a*x - b) + c^x + d

Detail solution

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

The answer is:

$a \log{\left(2 \right)} + c^{x} \log{\left(c \right)}$

The first derivative [src]

            x       
a*log(2) + c *log(c)

$$a \log{\left(2 \right)} + c^{x} \log{\left(c \right)}$$

Simplify

The second derivative [src]

 x    2   
c *log (c)

$$c^{x} \log{\left(c \right)}^{2}$$

Simplify

The third derivative [src]

 x    3   
c *log (c)

$$c^{x} \log{\left(c \right)}^{3}$$

Simplify