What is the derivative of w^{3/2}(w+ce^w) ?

The derivative of w^{3/2}(w+ce^w) is (3ce^ww^{1/2}+2ce^ww^{3/2}+5w^{3/2})/2

What is the first derivative of w^{3/2}(w+ce^w) ?

The first derivative of w^{3/2}(w+ce^w) is (3ce^ww^{1/2}+2ce^ww^{3/2}+5w^{3/2})/2

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derivative of

w^{\frac{3}{2}} (w + c e^{w})

\frac{3 c e ^{w} w ^{\frac{1}{2}} + 2 c e ^{w} w ^{\frac{3}{2}} + 5 w ^{\frac{3}{2}}}{2}

Solution steps

\frac{d}{d w} (w^{\frac{3}{2}} (w + c e^{w}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = w^{\frac{3}{2}}, g = w + c e^{w}

= \frac{d}{d w} (w^{\frac{3}{2}}) (w + c e^{w}) + \frac{d}{d w} (w + c e^{w}) w^{\frac{3}{2}}

\frac{d}{d w} (w^{\frac{3}{2}}) = \frac{3 w ^{\frac{1}{2}}}{2}

\frac{d}{d w} (w + c e^{w}) = 1 + c e^{w}

= \frac{3 w ^{\frac{1}{2}}}{2} (w + c e^{w}) + (1 + c e^{w}) w^{\frac{3}{2}}

Simplify

\frac{3 w ^{\frac{1}{2}}}{2} (w + c e^{w}) + (1 + c e^{w}) w^{\frac{3}{2}} : \frac{3 c e ^{w} w ^{\frac{1}{2}} + 2 c e ^{w} w ^{\frac{3}{2}} + 5 w ^{\frac{3}{2}}}{2}

= \frac{3 c e ^{w} w ^{\frac{1}{2}} + 2 c e ^{w} w ^{\frac{3}{2}} + 5 w ^{\frac{3}{2}}}{2}

\frac{d}{d x} (ln (x^{3} + 3))

x \to 0 lim (\frac{x}{x - 1})

x \to 0 lim (x - 4)

\int \frac{3 x ^{2} + 2 x - 3}{x ^{3} - x} d x

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

What is the derivative of w^{3/2}(w+ce^w) ?
The derivative of w^{3/2}(w+ce^w) is (3ce^ww^{1/2}+2ce^ww^{3/2}+5w^{3/2})/2
What is the first derivative of w^{3/2}(w+ce^w) ?
The first derivative of w^{3/2}(w+ce^w) is (3ce^ww^{1/2}+2ce^ww^{3/2}+5w^{3/2})/2