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
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How to use it?
- Derivative of:
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Derivative of 5^(2*x)
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Derivative of t-sint
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Derivative of (x-2)/(x+3)
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Derivative of x^2/(x^2+3)
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Identical expressions
- five ^sinx-cosx
- 5 to the power of sinus of x minus co sinus of e of x
- five to the power of sinus of x minus co sinus of e of x
- 5sinx-cosx
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Similar expressions
- 5^sinx+cosx
Derivative of 5^sinx-cosx
The solution
You have entered
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sin(x) 5 - cos(x)
$$5^{\sin{\left(x \right)}} - \cos{\left(x \right)}$$
5^sin(x) - cos(x)
Detail solution
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Differentiate term by term:
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Let .
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Then, apply the chain rule. Multiply by :
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The derivative of sine is cosine:
The result of the chain rule is:
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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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The derivative of cosine is negative sine:
So, the result is:
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The result is:
The answer is:
The first derivative
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sin(x) 5 *cos(x)*log(5) + sin(x)
$$5^{\sin{\left(x \right)}} \log{\left(5 \right)} \cos{\left(x \right)} + \sin{\left(x \right)}$$
The second derivative
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sin(x) 2 2 sin(x) 5 *cos (x)*log (5) - 5 *log(5)*sin(x) + cos(x)
$$- 5^{\sin{\left(x \right)}} \log{\left(5 \right)} \sin{\left(x \right)} + 5^{\sin{\left(x \right)}} \log{\left(5 \right)}^{2} \cos^{2}{\left(x \right)} + \cos{\left(x \right)}$$
The third derivative
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sin(x) 3 3 sin(x) sin(x) 2 -sin(x) + 5 *cos (x)*log (5) - 5 *cos(x)*log(5) - 3*5 *log (5)*cos(x)*sin(x)
$$- 3 \cdot 5^{\sin{\left(x \right)}} \log{\left(5 \right)}^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 5^{\sin{\left(x \right)}} \log{\left(5 \right)}^{3} \cos^{3}{\left(x \right)} - 5^{\sin{\left(x \right)}} \log{\left(5 \right)} \cos{\left(x \right)} - \sin{\left(x \right)}$$