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Derivative of:
Derivative of 1^3*sqrt(x)
Derivative of (x^2+1)/(x^2-1)
Derivative of x^3+2
Derivative of x^2+4
Integral of d{x}:
y(x)
y(x)
Identical expressions
y(x)=-6e^(five *t)-5ln5x
y(x) equally minus 6e to the power of (5 multiply by t) minus 5ln5x
y(x) equally minus 6e to the power of (five multiply by t) minus 5ln5x
y(x)=-6e(5*t)-5ln5x
yx=-6e5*t-5ln5x
y(x)=-6e^(5t)-5ln5x
y(x)=-6e(5t)-5ln5x
yx=-6e5t-5ln5x
yx=-6e^5t-5ln5x
Similar expressions
y(x)=-6e^(5*t)+5ln5x
y(x)=+6e^(5*t)-5ln5x

The derivative of the function/ y(x)=-6e^(5*t)-5ln5x

Derivative of y(x)=-6e^(5*t)-5ln5x

The solution

You have entered [src]

     5*t             
- 6*E    - 5*log(5*x)

- 6 e^{5 t} - 5 \log{\left(5 x \right)}

-6*exp(5*t) - 5*log(5*x)

Detail solution

Differentiate $- 6 e^{5 t} - 5 \log{\left(5 x \right)}$ term by term:
1. The derivative of the constant $- 6 e^{5 t}$ is zero.
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 5 x$ .
  2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$ :
    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: $5$
    The result of the chain rule is:
    
    $\frac{1}{x}$
  So, the result is: $- \frac{5}{x}$
The result is: $- \frac{5}{x}$

The answer is:

- \frac{5}{x}

The first derivative [src]

-5 
---
 x

- \frac{5}{x}

Simplify

The second derivative [src]

5 
--
 2
x

\frac{5}{x^{2}}

Simplify

The third derivative [src]

-10 
----
  3 
 x

- \frac{10}{x^{3}}

Simplify