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:
- Derivative of sinx^4
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Derivative of 3xlogx
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Derivative of 2sinx+3cosx
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Derivative of y=sin(0.5*x)
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Identical expressions
- 2sinx+3cosx
- 2 sinus of x plus 3 co sinus of e of x
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Similar expressions
- 2*sin(x)+3*cos(x)
- y=(2*sin(x)+3*cos(x))*x^2
- (2*sinx+3*cosx)*x^2
- 2sinx-3cosx
- -13^0,5(2sin(x)+3cos(x))exp^(13^0.5)(2cos(x)-3sin(x))
Derivative of 2sinx+3cosx
The solution
You have entered
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2*sin(x) + 3*cos(x)
$$2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$
d --(2*sin(x) + 3*cos(x)) dx
$$\frac{d}{d x} \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)$$
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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The derivative of sine is cosine:
So, the result 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:
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The answer is:
The first derivative
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-3*sin(x) + 2*cos(x)
$$- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}$$
The second derivative
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-(2*sin(x) + 3*cos(x))
$$- (2 \sin{\left(x \right)} + 3 \cos{\left(x \right)})$$
The third derivative
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-2*cos(x) + 3*sin(x)
$$3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}$$
The graph