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 4*e^(2*x)
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Derivative of -(3*pi*cos(pi*t/6))/2
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Derivative of (2x-1)^3
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Derivative of (x+4)/(x-1)
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Identical expressions
- 5sinx+3cosx
- 5 sinus of x plus 3 co sinus of e of x
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Similar expressions
- 3(x-1,25)sinx+3cosx+2
- 5*sin(x)+3*cos(x)
- 5sinx-3cosx
Derivative of 5sinx+3cosx
The solution
You have entered
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5*sin(x) + 3*cos(x)
$$5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$
d --(5*sin(x) + 3*cos(x)) dx
$$\frac{d}{d x} \left(5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)$$
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) + 5*cos(x)
$$- 3 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$
The second derivative
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-(3*cos(x) + 5*sin(x))
$$- (5 \sin{\left(x \right)} + 3 \cos{\left(x \right)})$$
The third derivative
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-5*cos(x) + 3*sin(x)
$$3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$$
The graph