What is the derivative of f(x)=x^{7/2}(3-4x^3) ?

The derivative of f(x)=x^{7/2}(3-4x^3) is (21x^{5/2}-52x^{11/2})/2

What is the first derivative of f(x)=x^{7/2}(3-4x^3) ?

The first derivative of f(x)=x^{7/2}(3-4x^3) is (21x^{5/2}-52x^{11/2})/2

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derivative of

f (x) = x^{\frac{7}{2}} (3 - 4 x^{3})

\frac{21 x ^{\frac{5}{2}} - 52 x ^{\frac{11}{2}}}{2}

Solution steps

\frac{d}{d x} (x^{\frac{7}{2}} (3 - 4 x^{3}))

Apply the Product Rule:

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

f = x^{\frac{7}{2}}, g = 3 - 4 x^{3}

= \frac{d}{d x} (x^{\frac{7}{2}}) (3 - 4 x^{3}) + \frac{d}{d x} (3 - 4 x^{3}) x^{\frac{7}{2}}

\frac{d}{d x} (x^{\frac{7}{2}}) = \frac{7 x ^{\frac{5}{2}}}{2}

\frac{d}{d x} (3 - 4 x^{3}) = - 12 x^{2}

= \frac{7 x ^{\frac{5}{2}}}{2} (3 - 4 x^{3}) + (- 12 x^{2}) x^{\frac{7}{2}}

Simplify

\frac{7 x ^{\frac{5}{2}}}{2} (3 - 4 x^{3}) + (- 12 x^{2}) x^{\frac{7}{2}} : \frac{21 x ^{\frac{5}{2}} - 52 x ^{\frac{11}{2}}}{2}

= \frac{21 x ^{\frac{5}{2}} - 52 x ^{\frac{11}{2}}}{2}

\frac{\partial}{\partial x} (\frac{1}{2 - x})

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

\int_{1}^{2} (6 - x^{2}) - (8 - 3 x) d x

6 x^{2} + x y + 3 y^{2} = 40

\int t arcsin (t) d t

What is the derivative of f(x)=x^{7/2}(3-4x^3) ?
The derivative of f(x)=x^{7/2}(3-4x^3) is (21x^{5/2}-52x^{11/2})/2
What is the first derivative of f(x)=x^{7/2}(3-4x^3) ?
The first derivative of f(x)=x^{7/2}(3-4x^3) is (21x^{5/2}-52x^{11/2})/2