What is the derivative of 5x^3sqrt(25-x^2) ?

The derivative of 5x^3sqrt(25-x^2) is (5(-4x^4+75x^2))/(sqrt(25-x^2))

What is the first derivative of 5x^3sqrt(25-x^2) ?

The first derivative of 5x^3sqrt(25-x^2) is (5(-4x^4+75x^2))/(sqrt(25-x^2))

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\frac{d}{d x} (5 x^{3} 25 - x^{2})

\frac{5 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (5 x^{3} 25 - x^{2})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{3} 25 - x^{2})

Apply the Product Rule:

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

f = x^{3}, g = 25 - x^{2}

= 5 (\frac{d}{d x} (x^{3}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{3})

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

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 5 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3})

Simplify

5 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3}) : \frac{5 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

= \frac{5 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

\frac{d y}{d x} = \frac{y - 1}{x ^{2}}

\int x cos (x y) + 1 d y

12

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

x e^{x}

What is the derivative of 5x^3sqrt(25-x^2) ?
The derivative of 5x^3sqrt(25-x^2) is (5(-4x^4+75x^2))/(sqrt(25-x^2))
What is the first derivative of 5x^3sqrt(25-x^2) ?
The first derivative of 5x^3sqrt(25-x^2) is (5(-4x^4+75x^2))/(sqrt(25-x^2))