What is the derivative of x-cos(sqrt(x)) ?

The derivative of x-cos(sqrt(x)) is 1+(sin(sqrt(x)))/(2sqrt(x))

What is the first derivative of x-cos(sqrt(x)) ?

The first derivative of x-cos(sqrt(x)) is 1+(sin(sqrt(x)))/(2sqrt(x))

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\frac{d}{d x} (x - cos (x))

1 + \frac{sin ( x )}{2 x}

Solution steps

\frac{d}{d x} (x - cos (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} - \frac{d}{d x} (cos (x))

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (x)) = - \frac{sin ( x )}{2 x}

= 1 - (- \frac{sin ( x )}{2 x})

Simplify

= 1 + \frac{sin ( x )}{2 x}

\frac{d}{d x} ((x + 1) (x^{3} + x - 2))

\int \frac{5}{( x - 1 ) ( x ^{2} + 4 )} d x

2 x + 1, (1, 3)

8 x^{7} y + x^{8} y^{^{'}} = - 5 sec^{2} (x) tan (x)

\frac{d}{d x} (- x + y + 2)

What is the derivative of x-cos(sqrt(x)) ?
The derivative of x-cos(sqrt(x)) is 1+(sin(sqrt(x)))/(2sqrt(x))
What is the first derivative of x-cos(sqrt(x)) ?
The first derivative of x-cos(sqrt(x)) is 1+(sin(sqrt(x)))/(2sqrt(x))