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

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

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

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

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derivative of

3 x^{3} 25 - x^{2}

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

Solution steps

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

Take the constant out:

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

= 3 \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}

= 3 (\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}}

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

Simplify

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

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

\int_{6}^{8} \frac{70}{( x - 6 ) ^{3}} d x

1 - 3 x^{2}

f^{^{'}} (x) = f (x) (1 - f (x))

\int \frac{( 7 sin ( x ) + 4 sec ( x ) )}{tan ( x )} d x

f (x) = 200 + \frac{7}{x} + \frac{x ^{2}}{7}

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