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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{a \cdot b}{c \cdot x})

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

\int sin (x) (cos (x))^{5} d x

f (x) = 5 ln (4 x)

f (x) = \frac{x - 5}{( x + 3 ) ^{4}}

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