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Find the derivative of $\sin\left(3x^2-1\right)^2$

Step-by-step Solution

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Final Answer

$12x\sin\left(3x^2-1\right)\cos\left(3x^2-1\right)$
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Step-by-step Solution

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

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

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

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of sin(3x^2-1)^2. 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 the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. 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 (-1) is equal to zero.

Final Answer

$12x\sin\left(3x^2-1\right)\cos\left(3x^2-1\right)$

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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 sin(3x^2-1)^2 using the product ruleFind derivative of sin(3x^2-1)^2 using the quotient ruleFind derivative of sin(3x^2-1)^2 using logarithmic differentiationFind derivative of sin(3x^2-1)^2 using the definition

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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
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

How to improve your answer:

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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