What is (\partial)/(\partial x)(5sqrt(9x^2+16y^2)) ?

The answer to (\partial)/(\partial x)(5sqrt(9x^2+16y^2)) is (45x)/(sqrt(9x^2+16y^2))

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(\partial)/(\partial x)(5sqrt(9x^2+16y^2))

\frac{\partial}{\partial x} (5 9 x^{2} + 16 y^{2})

\frac{45 x}{9 x ^{2} + 16 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (5 9 x^{2} + 16 y^{2})

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (9 x^{2} + 16 y^{2})

Apply the chain rule:

\frac{1}{2 9 x ^{2} + 16 y ^{2}} \frac{\partial}{\partial x} (9 x^{2} + 16 y^{2})

= \frac{1}{2 9 x ^{2} + 16 y ^{2}} \frac{\partial}{\partial x} (9 x^{2} + 16 y^{2})

\frac{\partial}{\partial x} (9 x^{2} + 16 y^{2}) = 18 x

= 5 \cdot \frac{1}{2 9 x ^{2} + 16 y ^{2}} \cdot 18 x

Simplify

5 \cdot \frac{1}{2 9 x ^{2} + 16 y ^{2}} \cdot 18 x : \frac{45 x}{9 x ^{2} + 16 y ^{2}}

= \frac{45 x}{9 x ^{2} + 16 y ^{2}}

\int \frac{7}{x ( x ^{2} + 25 )} d x

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

\int csc^{4} (x) cot^{2} (x) d x

x \to 2 lim (5 x^{3} + x)

\frac{d}{d x} (\frac{x sin ( x )}{2 + cos ( x )})

What is (\partial)/(\partial x)(5sqrt(9x^2+16y^2)) ?
The answer to (\partial)/(\partial x)(5sqrt(9x^2+16y^2)) is (45x)/(sqrt(9x^2+16y^2))