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Find the derivative of $4x\sqrt{x^3y^7}+3xy^2\sqrt{x^3y^3}-7y\sqrt{x^5y^5}+\frac{x}{y}\sqrt{25x^3y^9}$

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Calculus: Derivatives 2 | Taking derivatives | Differential Calculus | Khan Academy

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Function Plot

Plotting: $4\left(\sqrt{x^{3}}\sqrt{y^{7}}+x\left(\frac{3}{2}\sqrt{x}\sqrt{y^{7}}+\frac{7}{2}\sqrt{x^{3}}\sqrt{y^{5}}\right)\right)+3\left(\sqrt{y^{7}}\sqrt{x^{3}}+x\left(2y\sqrt{x^{3}}\sqrt{y^{3}}+y^2\left(\frac{3}{2}\sqrt{x}\sqrt{y^{3}}+\frac{3}{2}\sqrt{x^{3}}\sqrt{y}\right)\right)\right)-7\left(\sqrt{x^{5}}\sqrt{y^{5}}+y\left(\frac{5}{2}\sqrt{x^{3}}\sqrt{y^{5}}+\frac{5}{2}\sqrt{x^{5}}\sqrt{y^{3}}\right)\right)+5\left(\frac{5}{2}\sqrt{x^{3}}\sqrt{y^{7}}+\frac{7}{2}\sqrt{x^{5}}\sqrt{y^{5}}\right)$

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a
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x
y
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.
(◻)
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◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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