What is the derivative of 4sqrt(y^2+7x^2) ?

The derivative of 4sqrt(y^2+7x^2) is (4y)/(sqrt(y^2+7x^2))

What is the first derivative of 4sqrt(y^2+7x^2) ?

The first derivative of 4sqrt(y^2+7x^2) is (4y)/(sqrt(y^2+7x^2))

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derivative of

4 y^{2} + 7 x^{2}

\frac{4 y}{y ^{2} + 7 x ^{2}}

Solution steps

\frac{d}{d y} (4 y^{2} + 7 x^{2})

Treat

x

as a constant

Take the constant out:

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

= 4 \frac{d}{d y} (y^{2} + 7 x^{2})

Apply the chain rule:

\frac{1}{2 y ^{2} + 7 x ^{2}} \frac{d}{d y} (y^{2} + 7 x^{2})

= \frac{1}{2 y ^{2} + 7 x ^{2}} \frac{d}{d y} (y^{2} + 7 x^{2})

\frac{d}{d y} (y^{2} + 7 x^{2}) = 2 y

= 4 \cdot \frac{1}{2 y ^{2} + 7 x ^{2}} \cdot 2 y

Simplify

4 \cdot \frac{1}{2 y ^{2} + 7 x ^{2}} \cdot 2 y : \frac{4 y}{y ^{2} + 7 x ^{2}}

= \frac{4 y}{y ^{2} + 7 x ^{2}}

\frac{\partial}{\partial x} (2 x y^{6} + x^{4} y^{8})

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

\int 8 sin^{5} (x) cos (x) d x

(2 - 3 x) cos (3 x)

What is the derivative of 4sqrt(y^2+7x^2) ?
The derivative of 4sqrt(y^2+7x^2) is (4y)/(sqrt(y^2+7x^2))
What is the first derivative of 4sqrt(y^2+7x^2) ?
The first derivative of 4sqrt(y^2+7x^2) is (4y)/(sqrt(y^2+7x^2))