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f(x)=4x^6+7x^5+1

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Derivative of:
Derivative of f(x)=4x^6+7x^5+1
Derivative of cot(cos(2))+((sin(6*x)^(2))/cos(12*x))*(1/6)
Derivative of (2*x+3)^5
Derivative of x^-tan(x)
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=4x^ six +7x^ five + one
f(x) equally 4x to the power of 6 plus 7x to the power of 5 plus 1
f(x) equally 4x to the power of six plus 7x to the power of five plus one
f(x)=4x6+7x5+1
fx=4x6+7x5+1
f(x)=4x⁶+7x⁵+1
fx=4x^6+7x^5+1
Similar expressions
f(x)=4x^6+7x^5-1
f(x)=4x^6-7x^5+1

The derivative of the function/ f(x)=4x^6+7x^5+1

Derivative of f(x)=4x^6+7x^5+1

The solution

You have entered [src]

   6      5    
4*x  + 7*x  + 1

$$\left(4 x^{6} + 7 x^{5}\right) + 1$$

4*x^6 + 7*x^5 + 1

Detail solution

Differentiate $\left(4 x^{6} + 7 x^{5}\right) + 1$ term by term:
1. Differentiate $4 x^{6} + 7 x^{5}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
    So, the result is: $24 x^{5}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
    So, the result is: $35 x^{4}$
  The result is: $24 x^{5} + 35 x^{4}$
2. The derivative of the constant $1$ is zero.
The result is: $24 x^{5} + 35 x^{4}$
Now simplify:

$x^{4} \left(24 x + 35\right)$

The answer is:

$x^{4} \left(24 x + 35\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    5       4
24*x  + 35*x

$$24 x^{5} + 35 x^{4}$$

Simplify

The second derivative [src]

    3          
20*x *(7 + 6*x)

$$20 x^{3} \left(6 x + 7\right)$$

Simplify

The third derivative [src]

    2          
60*x *(7 + 8*x)

$$60 x^{2} \left(8 x + 7\right)$$

Simplify

The graph

Derivative of f(x)=4x^6+7x^5+1