What is the derivative of 4x^2sqrt(25-x^2) ?

The derivative of 4x^2sqrt(25-x^2) is (4(-3x^3+50x))/(sqrt(25-x^2))

What is the first derivative of 4x^2sqrt(25-x^2) ?

The first derivative of 4x^2sqrt(25-x^2) is (4(-3x^3+50x))/(sqrt(25-x^2))

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derivative of

4 x^{2} 25 - x^{2}

\frac{4 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (4 x^{2} 25 - x^{2})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{2} 25 - x^{2})

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 (2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2}) : \frac{4 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

= \frac{4 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

n = 1 \sum \infty \frac{6}{( 3 n + 1 ) ^{2}}

y^{^{''}} = e^{x}

\int_{0}^{16} x x d x

f (x) = ln (x^{2} - 4 x + 1)

y^{^{'}} + 5 x y = 6 x

What is the derivative of 4x^2sqrt(25-x^2) ?
The derivative of 4x^2sqrt(25-x^2) is (4(-3x^3+50x))/(sqrt(25-x^2))
What is the first derivative of 4x^2sqrt(25-x^2) ?
The first derivative of 4x^2sqrt(25-x^2) is (4(-3x^3+50x))/(sqrt(25-x^2))