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# Find the derivative of $\sqrt[3]{\sin\left(xy\right)-x^2}$

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##  Final Answer

$\frac{y\cos\left(xy\right)-2x}{3\sqrt[3]{\left(\sin\left(xy\right)-x^2\right)^{2}}}$
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##  Step-by-step Solution 

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1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{3}\left(\sin\left(xy\right)-x^2\right)^{-\frac{2}{3}}\frac{d}{dx}\left(\sin\left(xy\right)-x^2\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{1}{3}\left(\sin\left(xy\right)-x^2\right)^{-\frac{2}{3}}\frac{d}{dx}\left(\sin\left(xy\right)-x^2\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of (sin(xy)-x^2)^1/3. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

##  Final Answer

$\frac{y\cos\left(xy\right)-2x}{3\sqrt[3]{\left(\sin\left(xy\right)-x^2\right)^{2}}}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of (sinxy+-1x^2)^0.3333 using the product ruleFind derivative of (sinxy+-1x^2)^0.3333 using the quotient ruleFind derivative of (sinxy+-1x^2)^0.3333 using logarithmic differentiationFind derivative of (sinxy+-1x^2)^0.3333 using the definition

SnapXam A2

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
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

### 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.

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