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Derivative of tgx^2
Derivative of y=x^5-x^4+x^3-x^2+x-1
Derivative of y=(x^5-4x^2)^49
Derivative of y=(x^5-2x)^2
Identical expressions
y=(x^ five -4x^ two)^ forty-nine
y equally (x to the power of 5 minus 4x squared ) to the power of 49
y equally (x to the power of five minus 4x to the power of two) to the power of forty minus nine
y=(x5-4x2)49
y=x5-4x249
y=(x⁵-4x²)⁴9
y=(x to the power of 5-4x to the power of 2) to the power of 49
y=x^5-4x^2^49
Similar expressions
y=(x^5+4x^2)^49

The derivative of the function/ y=(x^5-4x^2)^49

Derivative of y=(x^5-4x^2)^49

The solution

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           49
/ 5      2\  
\x  - 4*x /

$$\left(x^{5} - 4 x^{2}\right)^{49}$$

(x^5 - 4*x^2)^49

Detail solution

Let $u = x^{5} - 4 x^{2}$ .
Apply the power rule: $u^{49}$ goes to $49 u^{48}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{5} - 4 x^{2}\right)$ :
1. Differentiate $x^{5} - 4 x^{2}$ term by term:
  1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $- 8 x$
  The result is: $5 x^{4} - 8 x$
The result of the chain rule is:

$49 \left(5 x^{4} - 8 x\right) \left(x^{5} - 4 x^{2}\right)^{48}$
Now simplify:

$x^{97} \left(x^{3} - 4\right)^{48} \left(245 x^{3} - 392\right)$

The answer is:

$x^{97} \left(x^{3} - 4\right)^{48} \left(245 x^{3} - 392\right)$

The graph

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The first derivative [src]

           48                  
/ 5      2\   /              4\
\x  - 4*x /  *\-392*x + 245*x /

$$\left(245 x^{4} - 392 x\right) \left(x^{5} - 4 x^{2}\right)^{48}$$

Simplify

The second derivative [src]

                 47 /              2                        \
     96 /      3\   |   /        3\    /      3\ /        3\|
196*x  *\-4 + x /  *\12*\-8 + 5*x /  + \-4 + x /*\-2 + 5*x //

$$196 x^{96} \left(x^{3} - 4\right)^{47} \left(\left(x^{3} - 4\right) \left(5 x^{3} - 2\right) + 12 \left(5 x^{3} - 8\right)^{2}\right)$$

Simplify

The third derivative [src]

                 46 /               3                 2                                       \
     95 /      3\   |    /        3\       3 /      3\       /        3\ /      3\ /        3\|
588*x  *\-4 + x /  *\188*\-8 + 5*x /  + 5*x *\-4 + x /  + 48*\-8 + 5*x /*\-4 + x /*\-2 + 5*x //

$$588 x^{95} \left(x^{3} - 4\right)^{46} \left(5 x^{3} \left(x^{3} - 4\right)^{2} + 48 \left(x^{3} - 4\right) \left(5 x^{3} - 8\right) \left(5 x^{3} - 2\right) + 188 \left(5 x^{3} - 8\right)^{3}\right)$$

Simplify

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