👉 Try now NerdPal! Our new math app on iOS and Android
Calculators Topics Solving Methods Step Checker
Book solutions
Algebra Baldor
Go Premium Topics

Find the derivative $\frac{d}{dh}\left(\frac{v}{\left(\sqrt{2}\right)^2+\left(\sqrt{7}\frac{h}{\sqrt{3}}+\sqrt{2}\frac{h}{\sqrt{3}}\right)^2}+\sqrt{2}\left(\sqrt{7}\frac{h}{\sqrt{3}}+\sqrt{2}\frac{h}{\sqrt{3}}\right)\right)$ using the sum rule

Step-by-step Solution

Go!
Math mode
Text mode
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
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

Solution

Formulas

Videos

Final Answer

$\frac{-10.988877vh}{\left(2+5.494438h^2\right)^2}+3.314947$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Simplifying

$\frac{d}{dh}\left(\frac{v}{\left(\sqrt{2}\right)^2+\left(\sqrt{7}\left(\frac{h}{\sqrt{3}}\right)+\sqrt{2}\left(\frac{h}{\sqrt{3}}\right)\right)^2}+\sqrt{2}\left(\sqrt{7}\left(\frac{h}{\sqrt{3}}\right)+\sqrt{2}\left(\frac{h}{\sqrt{3}}\right)\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dh}\left(\frac{v}{\left(\sqrt{2}\right)^2+\left(\sqrt{7}\left(\frac{h}{\sqrt{3}}\right)+\sqrt{2}\left(\frac{h}{\sqrt{3}}\right)\right)^2}+\sqrt{2}\left(\sqrt{7}\left(\frac{h}{\sqrt{3}}\right)+\sqrt{2}\left(\frac{h}{\sqrt{3}}\right)\right)\right)$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dh(v/(2^1/2^2+(h/(3^1/2)7^1/2+h/(3^1/2)2^1/2)^2)+2^1/2(h/(3^1/2)7^1/2+h/(3^1/2)2^1/2)) using the sum rule. Simplifying. Simplify the derivative by applying the properties of logarithms. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

Final Answer

$\frac{-10.988877vh}{\left(2+5.494438h^2\right)^2}+3.314947$

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 (v/(2^0.5^2+(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)^2)+2^0.5(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)) using the product ruleFind derivative of (v/(2^0.5^2+(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)^2)+2^0.5(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)) using the quotient ruleFind derivative of (v/(2^0.5^2+(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)^2)+2^0.5(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)) using logarithmic differentiationFind derivative of (v/(2^0.5^2+(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)^2)+2^0.5(h/(3^0.5)7^0.5+h/(3^0.5)2^0.5)) using the definition

Give us your feedback!

Function Plot

Plotting: $\frac{-10.988877vh}{\left(2+5.494438h^2\right)^2}+3.314947$

SnapXam A2
Answer Assistant

beta
Got a different 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
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

How to improve your answer:

Similar Problems Solved

Find the derivative

$\frac{d}{dx}\left(2x-1\cdot 4\cdot \ln\left(x+2\right)\right)$

Find the derivative

$\frac{d}{dx}\left(\pi100^2=0\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{\ln\left(x^2\right)}{x^2}\right)$

Find the derivative

$\frac{d}{dx}\left(e^{8x}+4x+e^{8x}\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$

Find the derivative

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

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

6. See formulas

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot password?

Supercharge your math learning



Register here if you don't have an account.
Forgot password?

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account