What is the derivative of x^4-(x^8/6-x^2sin(x^2)) ?

The derivative of x^4-(x^8/6-x^2sin(x^2)) is 4x^3-(4x^7)/3-2xsin(x^2)-2x^3cos(x^2)

What is the first derivative of x^4-(x^8/6-x^2sin(x^2)) ?

The first derivative of x^4-(x^8/6-x^2sin(x^2)) is 4x^3-(4x^7)/3-2xsin(x^2)-2x^3cos(x^2)

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\frac{d}{d x} (x^{4} - \frac{x ^{8}}{6} - x^{2} sin (x^{2}))

4 x^{3} - \frac{4 x ^{7}}{3} - 2 x sin (x^{2}) - 2 x^{3} cos (x^{2})

Solution steps

\frac{d}{d x} (x^{4} - \frac{x ^{8}}{6} - x^{2} sin (x^{2}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (\frac{x ^{8}}{6}) - \frac{d}{d x} (x^{2} sin (x^{2}))

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (\frac{x ^{8}}{6}) = \frac{4 x ^{7}}{3}

\frac{d}{d x} (x^{2} sin (x^{2})) = 2 x sin (x^{2}) + 2 x^{3} cos (x^{2})

= 4 x^{3} - \frac{4 x ^{7}}{3} - (2 x sin (x^{2}) + 2 x^{3} cos (x^{2}))

Simplify

= 4 x^{3} - \frac{4 x ^{7}}{3} - 2 x sin (x^{2}) - 2 x^{3} cos (x^{2})

\int (5 x + 4)^{3} d x

\frac{\partial}{\partial x} (sin^{2} (t))

n = 0 \sum \infty \frac{n}{( \frac{3}{2} ) ^{n}}

\frac{( s + 1 ) ^{3}}{s ^{4}}

\int t d t

What is the derivative of x^4-(x^8/6-x^2sin(x^2)) ?
The derivative of x^4-(x^8/6-x^2sin(x^2)) is 4x^3-(4x^7)/3-2xsin(x^2)-2x^3cos(x^2)
What is the first derivative of x^4-(x^8/6-x^2sin(x^2)) ?
The first derivative of x^4-(x^8/6-x^2sin(x^2)) is 4x^3-(4x^7)/3-2xsin(x^2)-2x^3cos(x^2)