Use Logarithmic Differentiation to Find the Derivative of the Function y = sin(5x)ln(x)
To find the derivative of the function y = sin(5x)ln(x), we will use logarithmic differentiation. This technique is especially useful when the function is a product of multiple functions or involves variable exponents. First, we take the natural logarithm of both sides: ln(y) = ln(sin(5x)) + ln(ln(x)) Next, we differentiate both sides with respect to […]
If h8 = 8 cos 8, find h8 and h8
To solve the expression where h8 is defined as h8 = 8 cos 8, we need to calculate the value of cos 8 first. The cosine function returns the ratio of the adjacent side to the hypotenuse in a right triangle, and its value ranges from -1 to 1. Using a calculator or a cosine […]
Find the volume of the sphere whose radius is 48 cm in terms of pi
To find the volume of a sphere, we use the formula: V = (4/3) × π × r³ Where V is the volume and r is the radius of the sphere. In this case, the radius r is given as 48 cm. Let’s substitute this value into the formula: V = (4/3) × π × […]
How to Find the Interval Where a Function is Increasing or Decreasing
To determine the intervals where a function is increasing or decreasing, you typically follow these steps: Find the derivative: Start by taking the derivative of the function, which gives you the rate of change of the function. Set the derivative to zero: Solve the equation where the derivative equals zero. This step helps you find […]
If cos 5, 13 tan 0, what is sin?
To find the value of sin in the context given, we first need to clarify the scenario. It appears that we are supposed to analyze the relationships between the trigonometric functions: cosine (cos), tangent (tan), and sine (sin). We know that: tan 0 = 0, since the tangent of 0 degrees (or radians) is zero. […]
Evaluate the function rule for the given value y = 15 – 3x for x = 3
To evaluate the function rule y = 15 – 3x when x = 3, we need to substitute the value of x into the equation. Here’s how it works: Start with the function: y = 15 – 3x. Substitute 3 for x: y = 15 – 3(3). Multiply: 3(3) = 9. Now, the equation looks […]
Solve for x: 3x + 1 = 2x + 4
To solve the equation 3x + 1 = 2x + 4, we want to isolate the variable x. We can start by getting all the terms with x on one side and the constant terms on the other side. 1. First, let’s subtract 2x from both sides: 3x + 1 – 2x = 2x + […]
What is the value of c in the quadratic equation 3x² + 5x + 7 = 0?
In the given quadratic equation, which is written in the standard form of ax² + bx + c = 0, we can identify the coefficients that correspond to a, b, and c. In your equation, 3x² + 5x + 7 = 0: a = 3 b = 5 c = 7 Therefore, the value of […]
How to Find the Area of a Circle Using Diameter?
To find the area of a circle using the diameter, you can follow these simple steps: 1. **Know the Formula**: The area (A) of a circle can be calculated using the formula: A = πr², where r is the radius of the circle. 2. **Calculate the Radius**: The diameter (d) of a circle is twice […]
Consider the function f(x) = 6x. What is the value of the growth factor of the function?
The function f(x) = 6x is an exponential function where the base is 6. In general, the growth factor of an exponential function of the form f(x) = a * b^x, where ‘a’ is a constant and ‘b’ is the base, indicates how much the function grows for each unit increase in x. In this […]