What is expand Dx[(e^x+4)(x^2-1/2)] ?

The solution to expand Dx[(e^x+4)(x^2-1/2)] is De^xx^3-(De^xx)/2+4Dx^3-2Dx

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expand Dx[(e^x+4)(x^2-1/2)]

expand

D x [(e^{x} + 4) (x^{2} - \frac{1}{2})]

D e^{x} x^{3} - \frac{D e ^{x} x}{2} + 4 D x^{3} - 2 D x

Solution steps

D x ((e^{x} + 4) (x^{2} - \frac{1}{2}))

Remove parentheses:

(a) = a

= D x (e^{x} + 4) (x^{2} - \frac{1}{2})

Expand

(e^{x} + 4) (x^{2} - \frac{1}{2}) : e^{x} x^{2} - \frac{1}{2} e^{x} + 4 x^{2} - 2

= D x (e^{x} x^{2} - \frac{1}{2} e^{x} + 4 x^{2} - 2)

Expand

D x (e^{x} x^{2} - \frac{1}{2} e^{x} + 4 x^{2} - 2) : D e^{x} x^{3} - \frac{D e ^{x} x}{2} + 4 D x^{3} - 2 D x

= D e^{x} x^{3} - \frac{D e ^{x} x}{2} + 4 D x^{3} - 2 D x

5 (1 + sin (x))

(3 - 2 s)^{2}

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

(cos^{3} (t) + sin^{3} (t)) \cdot (3 cos (t) sin (t))

\frac{p ^{3} + 2 p + 1}{p ^{2} ( p ^{2} + 2 )}

What is expand Dx[(e^x+4)(x^2-1/2)] ?
The solution to expand Dx[(e^x+4)(x^2-1/2)] is De^xx^3-(De^xx)/2+4Dx^3-2Dx