Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of x^5-1/(15x^5)
- Derivative of y=log*2(log*3(log*5x))
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Derivative of log5(4x-3)
- Derivative of sqrt(tan(x))
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Identical expressions
- y=log* two (log* three (log*5x))
- y equally logarithm of multiply by 2( logarithm of multiply by 3( logarithm of multiply by 5x))
- y equally logarithm of multiply by two ( logarithm of multiply by three ( logarithm of multiply by 5x))
- y=log2(log3(log5x))
- y=log2log3log5x
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Similar expressions
- y=log2(log3(log5x))
- y=log^2(log^3(log^5x))
Derivative of y=log*2(log*3(log*5x))
The solution
You have entered
[src]
log(2)*log(3)*log(5*x)
$$\log{\left(2 \right)} \log{\left(3 \right)} \log{\left(5 x \right)}$$
d --(log(2)*log(3)*log(5*x)) dx
$$\frac{d}{d x} \log{\left(2 \right)} \log{\left(3 \right)} \log{\left(5 x \right)}$$
Detail solution
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The derivative of a constant times a function is the constant times the derivative of the function.
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Let .
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The derivative of is .
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Then, apply the chain rule. Multiply by :
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the power rule: goes to
So, the result is:
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The result of the chain rule is:
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So, the result is:
The answer is:
The first derivative
[src]
log(2)*log(3)
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x
$$\frac{\log{\left(2 \right)} \log{\left(3 \right)}}{x}$$
The second derivative
[src]
-log(2)*log(3)
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2
x
$$- \frac{\log{\left(2 \right)} \log{\left(3 \right)}}{x^{2}}$$