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Find the higher order ($2$) derivative of $\frac{1}{20}\sin\left(5x^2\right)-\frac{1}{4}\sin\left(x^2\right)$

Step-by-step Solution

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Final Answer

$-5x^2\sin\left(5x^2\right)+\frac{1}{2}\cos\left(5x^2\right)+x^2\sin\left(x^2\right)-\frac{1}{2}\cos\left(x^2\right)$
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Step-by-step Solution

Specify the solving method

1

Find the ($1$) derivative

$\frac{1}{2}x\cos\left(5x^2\right)-\frac{1}{2}x\cos\left(x^2\right)$
2

Find the ($2$) derivative

$-5x^2\sin\left(5x^2\right)+\frac{1}{2}\cos\left(5x^2\right)+x^2\sin\left(x^2\right)-\frac{1}{2}\cos\left(x^2\right)$

Final Answer

$-5x^2\sin\left(5x^2\right)+\frac{1}{2}\cos\left(5x^2\right)+x^2\sin\left(x^2\right)-\frac{1}{2}\cos\left(x^2\right)$

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 (0.05sin5x^2+-0.25sin(x^2)) using the product ruleFind derivative of (0.05sin5x^2+-0.25sin(x^2)) using the quotient ruleFind derivative of (0.05sin5x^2+-0.25sin(x^2)) using logarithmic differentiation

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Function Plot

Plotting: $-5x^2\sin\left(5x^2\right)+\frac{1}{2}\cos\left(5x^2\right)+x^2\sin\left(x^2\right)-\frac{1}{2}\cos\left(x^2\right)$

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5
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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

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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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