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Derivative of:
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Identical expressions
y=x^ two +3cosx
y equally x squared plus 3 co sinus of e of x
y equally x to the power of two plus 3 co sinus of e of x
y=x2+3cosx
y=x²+3cosx
y=x to the power of 2+3cosx
Similar expressions
y=x^2-3cosx

The derivative of the function/ y=x^2+3cosx

Derivative of y=x^2+3cosx

The solution

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 2           
x  + 3*cos(x)

$$x^{2} + 3 \cos{\left(x \right)}$$

x^2 + 3*cos(x)

Detail solution

Differentiate $x^{2} + 3 \cos{\left(x \right)}$ term by term:
1. Apply the power rule: $x^{2}$ goes to $2 x$
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: $2 x - 3 \sin{\left(x \right)}$

The answer is:

$2 x - 3 \sin{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3*sin(x) + 2*x

$$2 x - 3 \sin{\left(x \right)}$$

Simplify

The second derivative [src]

2 - 3*cos(x)

$$2 - 3 \cos{\left(x \right)}$$

Simplify

The third derivative [src]

3*sin(x)

$$3 \sin{\left(x \right)}$$

Simplify

The graph

Derivative of y=x^2+3cosx