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let f(x) = ax if a is a constant, then f'(x) = a if a is not constant, then f'(x) = ax' + a'x

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What is the function if the first derivative of a function is a constant?

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What is the derivative of 7x?

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First expand the equation to get the following:(ax+b)2 = (ax+b)*(ax+b) = a2x2+2abx+b2Now do the integral, remember a&b are just coefficients, so:∫a2x2 + 2abx + b2 dxSo this integral becomes the following after integrating each term:(a2/3)x3 + abx2 + b2x + CYou can always take the derivative of the answer to check & see if it is correct.


What is the derivitive of ln10x?

The derivative of ln(x) is 1/x. Therefore, by Chain Rule, we get:[ln(10x)]' = 1/10x * 10 = 1/xUsing this method, you can also infer that the derivative of ln(Ax) where A is any constant equals 1/x.


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How do you find gradient on a quadratic graph?

To find the gradient on a quadratic graph, you first need to determine the derivative of the quadratic function, which is typically in the form (y = ax^2 + bx + c). The derivative, (y' = 2ax + b), represents the gradient at any point (x) on the curve. By substituting a specific (x) value into the derivative, you can find the gradient at that particular point on the graph. This gradient indicates the slope of the tangent line to the curve at the chosen point.


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How do I calculate the first derivative of a function?

To calculate the first derivative of a function, you can follow these general steps: Identify the function: Determine the function for which you want to find the first derivative. Let's assume your function is denoted as f(x). Express the function: Write down the function in its general form, considering any constants or variables involved. For example, f(x) = 3x^2 + 2x - 1. Differentiate the function: Use differentiation rules to find the derivative of the function. The derivative represents the rate of change of the function with respect to the variable. For example, to differentiate f(x) = 3x^2 + 2x - 1, apply the power rule and the sum rule as follows: Power rule: For a term of the form ax^n, the derivative is d/dx(ax^n) = anx^(n-1). Sum rule: The derivative of a sum of functions is the sum of their derivatives. Applying these rules to the function f(x) = 3x^2 + 2x - 1: The derivative of the term 3x^2 is 6x (using the power rule). The derivative of the term 2x is 2 (using the power rule, where the exponent is 1). The derivative of the constant term -1 is 0 (as the derivative of a constant is always 0). So, the first derivative of f(x) = 3x^2 + 2x - 1 is f'(x) = 6x + 2. Simplify if necessary: If there are any further simplifications or rearrangements possible, apply them to obtain the final form of the first derivative. In summary, the process involves differentiating each term of the function with respect to the variable and then simplifying the resulting expression. Differentiation rules such as the power rule, sum rule, product rule, and chain rule can be used depending on the complexity of the function.