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

The derivative of y=2x^4sqrt(25-x^2) is (2(-5x^5+100x^3))/(sqrt(25-x^2))

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

The first derivative of y=2x^4sqrt(25-x^2) is (2(-5x^5+100x^3))/(sqrt(25-x^2))

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derivative of

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

\frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = 25 - x^{2}

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

Simplify

2 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4}) : \frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

= \frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

(ln (1 + x^{2}))^{^{'}}

\int (\frac{6}{x ^{3}}) d x

\frac{\partial}{\partial y} (6 x y^{2} - 6 x^{2} y + 5 x y)

x^{4} - 5 x^{2} + 4

\frac{d}{d x} (e^{s i n (2 x)} + sin (e^{2 x}))

What is the derivative of y=2x^4sqrt(25-x^2) ?
The derivative of y=2x^4sqrt(25-x^2) is (2(-5x^5+100x^3))/(sqrt(25-x^2))
What is the first derivative of y=2x^4sqrt(25-x^2) ?
The first derivative of y=2x^4sqrt(25-x^2) is (2(-5x^5+100x^3))/(sqrt(25-x^2))