What is (\partial)/(\partial x)((3x^2+5x+1)^{3/2}) ?

The answer to (\partial)/(\partial x)((3x^2+5x+1)^{3/2}) is (3(6x+5)(3x^2+5x+1)^{1/2})/2

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(\partial)/(\partial x)((3x^2+5x+1)^{3/2})

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

\frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

Solution steps

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (3 x^{2} + 5 x + 1)

= \frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (3 x^{2} + 5 x + 1)

\frac{\partial}{\partial x} (3 x^{2} + 5 x + 1) = 6 x + 5

= \frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} (6 x + 5)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

\int x \cdot \frac{5}{2} \cdot x^{2} + 7 d x

\int_{1}^{2} 3 x^{2} + 2 x + 1 d x

\int_{0}^{2} 2^{- x} d x

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y})

y^{2} y^{^{'}} = y^{3} - 3 x, y (0) = 2

What is (\partial)/(\partial x)((3x^2+5x+1)^{3/2}) ?
The answer to (\partial)/(\partial x)((3x^2+5x+1)^{3/2}) is (3(6x+5)(3x^2+5x+1)^{1/2})/2