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Find the derivative of $\left(\left(x^2+3\right)^5\right)^2$

Step-by-step Solution

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Solution

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Final Answer

$20\left(x^2+3\right)^{9}x$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\left(x^2+3\right)^{10}\right)$

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$\frac{d}{dx}\left(\left(x^2+3\right)^{10}\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of (x^2+3)^5^2. Simplify the derivative by applying the properties of logarithms. 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 the constant function (3) is equal to zero.

Final Answer

$20\left(x^2+3\right)^{9}x$

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 (x^2+3)^5^2 using the product ruleFind derivative of (x^2+3)^5^2 using the quotient ruleFind derivative of (x^2+3)^5^2 using logarithmic differentiationFind derivative of (x^2+3)^5^2 using the definition

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Function Plot

Plotting: $20\left(x^2+3\right)^{9}x$

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1
2
3
4
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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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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