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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

$6x\sin\left(6x^2-2\right)$
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Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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

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

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

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

Unlock the first 2 steps of this solution!

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

$6x\sin\left(6x^2-2\right)$
SnapXam A2
Answer Assistant

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Got another answer? Verify it!

Go!
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
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

Useful tips on how to improve your answer:

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

Main topic:

Differential Calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.08 s