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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int_{1}^{\infty} \frac{3}{x ^{3}} d x

\frac{\partial}{\partial x} (x^{3} - x^{2} + y^{3} - y^{2})

\int x e^{x^{2} - 1} d x

\int_{0}^{1} e^{x^{4}} d x

\int cos^{4} (x t a) n^{3} x d x

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