{eq}y=3^x {/eq} Question: Differentiate wrt x {eq}y=3^x {/eq} Derivative of a Power The derivative of a power comes directly related to the concept of the logarithm. We can obtain, the following general rule for the case of a constant base, ...
Part (iii): Differentiate √(3)x2 1. Rewrite the function: The cube root can be expressed as a power: √(3)x2=x23.2. Apply the power rule: ddx(x23)=23x23−1=23x−13 Solution for Part (iii):ddx(√(3)x2)=23x−13 --- Summary of Solutions:1. ddx(3x−5)=−15x...
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the need to find the derivative of a function is needed than in most of the cases some functions are used or seen more it is better to memorize the derivative of such functions. One of the most used functions isf(x)=xnwherenis the power ofx. The derivative of such function is given ...
Differentiate the function f(x)=ex+xe Differentiation Strategy: The derivative of the expression of the given type is solved easily with the following two formulas: One is the power rule that is given by:ddx(xa)=a⋅xa−1another is the formula of differentiation of exponential function:ddx...
Apparent diffusion coefficient (ADC) of magnetic resonance imaging (MRI) is an indispensable imaging technique in clinical neuroimaging that quantitatively assesses the diffusivity of water molecules within tissues using diffusion-weighted imaging (DWI).
Step 3 Simplify the differentiated function: y = e^(-x) * (-1) gives y = -e^(-x). Therefore, this is the derivative of the negative exponential. References Cite This Article MLA Bourdin, Thomas. "How To Differentiate Negative Exponentials"sciencing.com, https://www.sciencing.com/differ...
Since the early diagnosis of lung cancer is very important for treatment, the accurate diagnosis of SPNs has much importance. The aim of this study was to evaluate the discriminant power of dual time point imaging (DTPI) PET/CT in the differentiation of malignant and benign FDG-avid solitary...
We will differentiate each term in the function f(x). 1. Differentiate √x: - Recall that √x=x1/2. - Using the power rule ddx(xn)=nxn−1: ddx(√x)=12x−12=12√x 2. Differentiate cotx: - The derivative of cotx is: ddx(cotx)=−csc2x 3. Differentiate −ex: - The ...
Answer to: Differentiate each of the following. 1. f (x) = ln (8 x - 5). 2. g (x) = e^{5 x}. 3. h (x) = 83 x. 4. y = log (x). By signing up,...