What is the derivative of 4x^{0.75}*(240-2x^{0.5}) ?

The derivative of 4x^{0.75}*(240-2x^{0.5}) is (4(180-2.5x))/(x^{0.25)(-2x+240)^{1/2}}

What is the first derivative of 4x^{0.75}*(240-2x^{0.5}) ?

The first derivative of 4x^{0.75}*(240-2x^{0.5}) is (4(180-2.5x))/(x^{0.25)(-2x+240)^{1/2}}

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\frac{d}{d x} (4 x^{0.75} \cdot (240 - 2 x)^{0.5})

\frac{4 ( 180 - 2.5 x )}{x ^{0.25} ( - 2 x + 240 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (4 x^{0.75} (240 - 2 x)^{0.5})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{0.75} (240 - 2 x)^{0.5})

Apply the Product Rule:

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

f = x^{0.75}, g = (240 - 2 x)^{0.5}

= 4 (\frac{d}{d x} (x^{0.75}) (240 - 2 x)^{0.5} + \frac{d}{d x} ((240 - 2 x)^{0.5}) x^{0.75})

\frac{d}{d x} (x^{0.75}) = \frac{0.75}{x ^{0.25}}

\frac{d}{d x} ((240 - 2 x)^{0.5}) = - \frac{1}{( 240 - 2 x ) ^{\frac{1}{2}}}

= 4 (\frac{0.75}{x ^{0.25}} (240 - 2 x)^{0.5} + (- \frac{1}{( 240 - 2 x ) ^{\frac{1}{2}}}) x^{0.75})

Simplify

4 (\frac{0.75}{x ^{0.25}} (240 - 2 x)^{\frac{1}{2}} + (- \frac{1}{( 240 - 2 x ) ^{\frac{1}{2}}}) x^{0.75}) : \frac{4 ( 180 - 2.5 x )}{x ^{0.25} ( - 2 x + 240 ) ^{\frac{1}{2}}}

= \frac{4 ( 180 - 2.5 x )}{x ^{0.25} ( - 2 x + 240 ) ^{\frac{1}{2}}}

\int_{- 3}^{- 1} \frac{5}{x ^{4}} d x

f (x) = \frac{27}{5 x ^{2}} - \frac{3}{2}, at x = 1

\int_{1}^{5} \frac{x ^{2} + 5}{6 x - x ^{2}} d x

\frac{d y}{d x} = \frac{( x y + x )}{y}

y^{^{''}} + 2 π y^{^{'}} + π^{2} y = 0

What is the derivative of 4x^{0.75}*(240-2x^{0.5}) ?
The derivative of 4x^{0.75}*(240-2x^{0.5}) is (4(180-2.5x))/(x^{0.25)(-2x+240)^{1/2}}
What is the first derivative of 4x^{0.75}*(240-2x^{0.5}) ?
The first derivative of 4x^{0.75}*(240-2x^{0.5}) is (4(180-2.5x))/(x^{0.25)(-2x+240)^{1/2}}