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Derivative of:
Derivative of (4-3*x)^7
Derivative of 3x²-2
Derivative of (x-5)^2*e^x-7
Derivative of x/(1+e^x)
Identical expressions
y=x^ seven -2cosx
y equally x to the power of 7 minus 2 co sinus of e of x
y equally x to the power of seven minus 2 co sinus of e of x
y=x7-2cosx
y=x⁷-2cosx
Similar expressions
y=x^7+2cosx

The derivative of the function/ y=x^7-2cosx

Derivative of y=x^7-2cosx

The solution

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 7           
x  - 2*cos(x)

$$x^{7} - 2 \cos{\left(x \right)}$$

x^7 - 2*cos(x)

Detail solution

Differentiate $x^{7} - 2 \cos{\left(x \right)}$ term by term:
1. Apply the power rule: $x^{7}$ goes to $7 x^{6}$
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: $2 \sin{\left(x \right)}$
The result is: $7 x^{6} + 2 \sin{\left(x \right)}$

The answer is:

$7 x^{6} + 2 \sin{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              6
2*sin(x) + 7*x

$$7 x^{6} + 2 \sin{\left(x \right)}$$

Simplify

The second derivative [src]

  /    5         \
2*\21*x  + cos(x)/

$$2 \left(21 x^{5} + \cos{\left(x \right)}\right)$$

Simplify

The third derivative [src]

  /               4\
2*\-sin(x) + 105*x /

$$2 \left(105 x^{4} - \sin{\left(x \right)}\right)$$

Simplify

The graph

Derivative of y=x^7-2cosx