What is the derivative of 1/4*x^2-((sin(2x^2)))/8 ?

The derivative of 1/4*x^2-((sin(2x^2)))/8 is (x-xcos(2x^2))/2

What is the first derivative of 1/4*x^2-((sin(2x^2)))/8 ?

The first derivative of 1/4*x^2-((sin(2x^2)))/8 is (x-xcos(2x^2))/2

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derivative of

\frac{1}{4} \cdot x^{2} - \frac{( sin ( 2 x ^{2} ) )}{8}

\frac{x - x cos ( 2 x ^{2} )}{2}

Solution steps

\frac{d}{d x} (\frac{1}{4} x^{2} - \frac{sin ( 2 x ^{2} )}{8})

Simplify

\frac{1}{4} x^{2} - \frac{sin ( 2 x ^{2} )}{8} : \frac{x ^{2}}{4} - \frac{sin ( 2 x ^{2} )}{8}

= \frac{d}{d x} (\frac{x ^{2}}{4} - \frac{sin ( 2 x ^{2} )}{8})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{2}}{4}) - \frac{d}{d x} (\frac{sin ( 2 x ^{2} )}{8})

\frac{d}{d x} (\frac{x ^{2}}{4}) = \frac{x}{2}

\frac{d}{d x} (\frac{sin ( 2 x ^{2} )}{8}) = \frac{x cos ( 2 x ^{2} )}{2}

= \frac{x}{2} - \frac{x cos ( 2 x ^{2} )}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{x - x cos ( 2 x ^{2} )}{2}

d er i v a t i v e sin^{4} (3 x - 4 x^{2})

d er i v a t i v e - (e^{- x})^{2}

d er i v a t i v e lo g_{10} (x - 1)

\frac{d}{d s} (3 s^{2})

d er i v a t i v e y = \frac{( x ^{5} + x ^{2} )}{( x ^{3} + 1 )}

What is the derivative of 1/4*x^2-((sin(2x^2)))/8 ?
The derivative of 1/4*x^2-((sin(2x^2)))/8 is (x-xcos(2x^2))/2
What is the first derivative of 1/4*x^2-((sin(2x^2)))/8 ?
The first derivative of 1/4*x^2-((sin(2x^2)))/8 is (x-xcos(2x^2))/2