Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of 3^x
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Derivative of x^(1/2)
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Derivative of x*atan(x)
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Derivative of -2
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Identical expressions
- y=sqrt4^x+ one /2x^ eight
- y equally square root of 4 to the power of x plus 1 divide by 2x to the power of 8
- y equally square root of 4 to the power of x plus one divide by 2x to the power of eight
- y=√4^x+1/2x^8
- y=sqrt4x+1/2x8
- y=sqrt4^x+1/2x⁸
- y=sqrt4^x+1 divide by 2x^8
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Similar expressions
- y=sqrt4^x-1/2x^8
Derivative of y=sqrt4^x+1/2x^8
The solution
You have entered
[src]
x 8
___ x
\/ 4 + --
2
$$\frac{x^{8}}{2} + \left(\sqrt{4}\right)^{x}$$
(sqrt(4))^x + x^8/2
Detail solution
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Differentiate term by term:
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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 is:
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Now simplify:
The answer is:
The first derivative
[src]
x
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7 2 / ___\
4*x + 4 *log\\/ 4 /
$$4^{\frac{x}{2}} \log{\left(\sqrt{4} \right)} + 4 x^{7}$$
The second derivative
[src]
x
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2 / ___\
6 4 *log(4)*log\\/ 4 /
28*x + --------------------
2
$$\frac{4^{\frac{x}{2}} \log{\left(4 \right)} \log{\left(\sqrt{4} \right)}}{2} + 28 x^{6}$$
The third derivative
[src]
x
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2 2 / ___\
5 4 *log (4)*log\\/ 4 /
168*x + ---------------------
4
$$\frac{4^{\frac{x}{2}} \log{\left(4 \right)}^{2} \log{\left(\sqrt{4} \right)}}{4} + 168 x^{5}$$
The graph