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Find the derivative of $a\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)^2$

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Solution

Final Answer

$2a\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)\left(2\left(bs^3x+2y\right)\left(bs^3+2\right)-18\left(4x+5y\right)\right)$
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Step-by-step Solution

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The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$a\frac{d}{dx}\left(\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)^2\right)$

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$a\frac{d}{dx}\left(\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)^2\right)$

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Learn how to solve problems step by step online. Find the derivative of a((bs^3x+2y)^2-(4x+5y)^2)^2. The derivative of a function multiplied by a constant 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}. 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 is equal to the constant times the derivative of the function.

Final Answer

$2a\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)\left(2\left(bs^3x+2y\right)\left(bs^3+2\right)-18\left(4x+5y\right)\right)$

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 a((bs^3+2y)^2+-1(4x+5y)^2)^2 using the product ruleFind derivative of a((bs^3+2y)^2+-1(4x+5y)^2)^2 using the quotient ruleFind derivative of a((bs^3+2y)^2+-1(4x+5y)^2)^2 using logarithmic differentiationFind derivative of a((bs^3+2y)^2+-1(4x+5y)^2)^2 using the definition

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Function Plot

Plotting: $2a\left(\left(bs^3x+2y\right)^2-\left(4x+5y\right)^2\right)\left(2\left(bs^3x+2y\right)\left(bs^3+2\right)-18\left(4x+5y\right)\right)$

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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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