What is the derivative of 28x(4x^2+9)^{5/2} ?

The derivative of 28x(4x^2+9)^{5/2} is 28((4x^2+9)^{5/2}+20x^2(4x^2+9)^{3/2})

What is the first derivative of 28x(4x^2+9)^{5/2} ?

The first derivative of 28x(4x^2+9)^{5/2} is 28((4x^2+9)^{5/2}+20x^2(4x^2+9)^{3/2})

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derivative of

28 x (4 x^{2} + 9)^{\frac{5}{2}}

28 ((4 x^{2} + 9)^{\frac{5}{2}} + 20 x^{2} (4 x^{2} + 9)^{\frac{3}{2}})

Solution steps

\frac{d}{d x} (28 x (4 x^{2} + 9)^{\frac{5}{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 28 \frac{d}{d x} (x (4 x^{2} + 9)^{\frac{5}{2}})

Apply the Product Rule:

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

f = x, g = (4 x^{2} + 9)^{\frac{5}{2}}

= 28 (\frac{d x}{d x} (4 x^{2} + 9)^{\frac{5}{2}} + \frac{d}{d x} ((4 x^{2} + 9)^{\frac{5}{2}}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((4 x^{2} + 9)^{\frac{5}{2}}) = 20 x (4 x^{2} + 9)^{\frac{3}{2}}

= 28 (1 \cdot (4 x^{2} + 9)^{\frac{5}{2}} + 20 x (4 x^{2} + 9)^{\frac{3}{2}} x)

Simplify

28 (1 \cdot (4 x^{2} + 9)^{\frac{5}{2}} + 20 x (4 x^{2} + 9)^{\frac{3}{2}} x) : 28 ((4 x^{2} + 9)^{\frac{5}{2}} + 20 x^{2} (4 x^{2} + 9)^{\frac{3}{2}})

= 28 ((4 x^{2} + 9)^{\frac{5}{2}} + 20 x^{2} (4 x^{2} + 9)^{\frac{3}{2}})

x lo g_{3} (x)

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

\frac{\partial}{\partial x} (4 y cos (x y))

x tan (x)

\int_{\frac{π}{2}}^{π} sin^{2} (x) d x

What is the derivative of 28x(4x^2+9)^{5/2} ?
The derivative of 28x(4x^2+9)^{5/2} is 28((4x^2+9)^{5/2}+20x^2(4x^2+9)^{3/2})
What is the first derivative of 28x(4x^2+9)^{5/2} ?
The first derivative of 28x(4x^2+9)^{5/2} is 28((4x^2+9)^{5/2}+20x^2(4x^2+9)^{3/2})