1. The derivative of the logarithmic function log_a(x) is given by the formula 1/(x * ln(a)).2. For any differentiable function f(x), the derivative of f(x), denoted as f'(x), is itself a new function, which is referred to as the derivative of f(x).3. The de...
The derivative of the logarithmic function is given by:f ' (x) = 1 / ( x ln(b) ) x is the function argument.b is the logarithm base.ln b is the natural logarithm of b.For example when:f (x) = log2(x)f ' (x) = 1 / ( x ln(2) )...
Derivative of log x Proof by First Principle We will prove that d/dx(logₐ x) = 1/(x ln a) using the first principle (definition of the derivative). Proof: Let us assume thatf(x)=logₐ x.By first principle,the derivative of afunctionf(x)(which is denoted by f'(x)) is gi...
∫lnxdx=∫tde^t=te^t-∫e^tdt=te^t-e^t=xlnx-x 所以∫logaxdx=1/lna*∫lnxdx=（xlnx-x）/lna 导数（Derivative），也叫导函数值。又名微商，是微积分中的重要基础概念。当函数y=f（x）的自变量x在一点x0上产生一个增量Δx时，函数输出值的增量Δy与自变量增量Δx的比值在Δx趋于0...
Derivative function: Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function. ...
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( log_{log_{sin(x)}^{x}}^{log_{x}^{cos(x)}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{(-sin(x))}{(cos(x))} - \frac{(1)log_{x}^{cos(x)}}...
Derivative of log[log(logx5)] with respect to x is A1xlogxlog(logx5) B1xlog(logx5) C5xlog(logx5) DNone of theseSubmit The derivative of log10x with respect to x2, is A12x2loge10 B2x2log10e C12x2loge10 Dnone of theseSubmit What is the derivative of log10(5x2+3) with ...
The derivative of log[log(logx)]w.r.t x is View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Raj...
Logarithm derivative When f(x) = logb(x) Then the derivative of f(x): f '(x) = 1 / (xln(b) ) For example: When f(x) = log2(x) Then the derivative of f(x): f '(x) = 1 / (xln(2) ) Logarithm integral The integral of logarithm of x: ...
Differentiate using the chain rule, which states that is where and . Tap for more steps... Step 1.1 To apply the Chain Rule, set as . Step 1.2 The derivative of with respect to is . Step 1.3 Replace all occurrences of with .Step...