To differentiate the function f(x)=a0xn+a1xn−1+a2xn−2+…+an−1x+an with respect to x, we will apply the power rule of differentiation to each term of the polynomial. 1. Identify the function: f(x)=a0xn+a1xn−1+a2xn−2+…+an−1x+an 2. Differentiate each term us...
Differentiate the power series for f(x) = xe^x. Use the result to find the sum of the infinite series: \sum_{n = 0}^{\infty}\frac{n + 1}{n!} Differentiate the power series for ln (1 + x) at x = 0 to obtain a series representation for the function f(x)...
Answer to: a) Differentiate y=\frac {e^x}{x}, y = \frac{e^x}{x^2}, y = \frac {e^x}{x^3} b) What do you anticipate the derivative of ...
doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS...
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...
(3) eix = (-sin(x) + icos(x)) / i (4) eix = cos(x) + isin(x) Just lost in circles. Technically, you didn't differentiate equation 1 -- you took the differential of each side. If you differentate equation 1 with respect to x, you get (2) eixi = -sin(x) + icos(x...
In summary, to differentiate y=e^x, we use the rule for differentiating the inverse of a function since the exponential function is the inverse of the natural logarithmic function. This gives us the derivative of e^x as e^x. For y=lnx, we can use implicit differentiation with the help ...
If you draw a figure you can easily check that the definitions agree in the intersection of the two half-planes x>0x>0 and y>0y>0, etc. While arg(x,y)arg(x,y) is only determined "up to 2πZ2πZ" its gradient ∇arg∇arg is a well defined vector field in R˙2R...
Next-generation sequencing (NGS) has advanced the application of high-throughput sequencing technologies in genetic and genomic variation analysis. Due to the large dynamic range of expression levels, RNA-seq is more prone to detect transcripts with low expression. It is clear that genes with no ...
3.h(x)=83x. 4.y=log(x). Chain Rule: Letq(x)andg(x)be functions ofxthen the derivative ofq(g(x))is given by chain rule, such that: ddxq(g(x))=q′(g(x))ddxg(x) The following rules are relevant to this problem: ...