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Derivative of:
Derivative of (x^2-4)^3
Derivative of 4√x
Derivative of x^2*5^x
Derivative of y=e^(3x)
Identical expressions
y=x^ six -3cosx
y equally x to the power of 6 minus 3 co sinus of e of x
y equally x to the power of six minus 3 co sinus of e of x
y=x6-3cosx
y=x⁶-3cosx
Similar expressions
y=x^6+3cosx

The derivative of the function/ y=x^6-3cosx

Derivative of y=x^6-3cosx

The solution

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 6           
x  - 3*cos(x)

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

x^6 - 3*cos(x)

Detail solution

Differentiate $x^{6} - 3 \cos{\left(x \right)}$ term by term:
1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $3 \sin{\left(x \right)}$
The result is: $6 x^{5} + 3 \sin{\left(x \right)}$

The answer is:

$6 x^{5} + 3 \sin{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              5
3*sin(x) + 6*x

$$6 x^{5} + 3 \sin{\left(x \right)}$$

Simplify

The second derivative [src]

  /    4         \
3*\10*x  + cos(x)/

$$3 \left(10 x^{4} + \cos{\left(x \right)}\right)$$

Simplify

The third derivative [src]

  /              3\
3*\-sin(x) + 40*x /

$$3 \left(40 x^{3} - \sin{\left(x \right)}\right)$$

Simplify

The graph

Derivative of y=x^6-3cosx