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Find the derivative $\frac{d}{da}\left(15a\left(a+1\right)^3-5a\left(\left(\left(a+1\right)^2\right)^3\right)^2\right)$ using the sum rule

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Solution

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Final Answer

$15\left(\left(a+1\right)^3+3a\left(a+1\right)^{2}\right)-5\left(\left(a+1\right)^{12}+12a\left(a+1\right)^{11}\right)$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{da}\left(15a\left(a+1\right)^3-5a\left(a+1\right)^{12}\right)$

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$\frac{d}{da}\left(15a\left(a+1\right)^3-5a\left(a+1\right)^{12}\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/da(15a(a+1)^3-5a(a+1)^2^3^2) using the sum rule. Simplify the derivative by applying the properties of logarithms. 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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=a and g=\left(a+1\right)^3.

Final Answer

$15\left(\left(a+1\right)^3+3a\left(a+1\right)^{2}\right)-5\left(\left(a+1\right)^{12}+12a\left(a+1\right)^{11}\right)$

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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 (15a+-5a) using the product ruleFind derivative of (15a+-5a) using the quotient ruleFind derivative of (15a+-5a) using logarithmic differentiationFind derivative of (15a+-5a) using the definition

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Function Plot

Plotting: $15\left(\left(a+1\right)^3+3a\left(a+1\right)^{2}\right)-5\left(\left(a+1\right)^{12}+12a\left(a+1\right)^{11}\right)$

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◻/◻
/
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◻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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Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

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