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y=sinx+x^2

Derivative of y=sinx+x^2

Function f() - derivative -N order at the point
v

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The solution

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          2
sin(x) + x 
x2+sin(x)x^{2} + \sin{\left(x \right)}
d /          2\
--\sin(x) + x /
dx             
ddx(x2+sin(x))\frac{d}{d x} \left(x^{2} + \sin{\left(x \right)}\right)
Detail solution
  1. Differentiate x2+sin(x)x^{2} + \sin{\left(x \right)} term by term:

    1. The derivative of sine is cosine:

      ddxsin(x)=cos(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

    2. Apply the power rule: x2x^{2} goes to 2x2 x

    The result is: 2x+cos(x)2 x + \cos{\left(x \right)}


The answer is:

2x+cos(x)2 x + \cos{\left(x \right)}

The graph
02468-8-6-4-2-1010200-100
The first derivative [src]
2*x + cos(x)
2x+cos(x)2 x + \cos{\left(x \right)}
The second derivative [src]
2 - sin(x)
sin(x)+2- \sin{\left(x \right)} + 2
The third derivative [src]
-cos(x)
cos(x)- \cos{\left(x \right)}
The graph
Derivative of y=sinx+x^2