Here you can see the derivative f'(x) and the second derivative f''(x) of some common functions.Notice how the slope of each function is the y-value of the derivative plotted below it.For example, move to where the sin(x) function slope flattens out (slope=0), then see that the...
Homework Statement Compute Derivative y = xx + sin(x) Homework EquationsThe Attempt at a Solution since I have x in the exponent (x^x), I multiply both sides by ln: ln y = ln xx + ln sin(x) the x in the exponent comes out into the front, right? y'/y = x ln x + ln sin...
Replies: 2 Forum:Engineering and Comp Sci Homework Help J Simple derivative of exponential function 1. Homework Statement Find derivative of y=e^(cos(t)+lnt) Homework EquationsThe Attempt at a Solution So just using the chain rule: y'=e^(cos(t)+lnt)*(-sin(t)+1/t) The answer in th...
tanx=sinxcosx cotx=cosxsinx 3)cscx=1sinx,among others. Answer and Explanation:1 Let us find the derivative ofy=sec(x). Let's redefine the function as a function of cosine. Thus we have {eq}y = \dfrac{1}{\cos x}... ...
Find the derivative {eq}y = log_7(sin(6x)) {/eq} Differentiation in calculus: The given function {eq}y= f(x) {/eq} is the composition of two functions so we'll use the chain rule. The chain rule is used for computing the derivative of the composition of two functions. The ...
=3(x2−1)2⋅2x Simplify=6x(x2−1)2 Enter your problem Popular Examples Frequently Asked Questions (FAQ) What is the derivative of (x^2-1)^3 ? The derivative of (x^2-1)^3 is 6x(x^2-1)^2 What is the first derivative of (x^2-1)^3 ?
Step 2: Find the second derivative d2ydx2 Now we will differentiate dydx again using the product rule. Let:- u=e6x- v=−3sin(3x)+6cos(3x) We need to find dudx and dvdx: 1. Differentiate u: dudx=6e6x 2. Differentiate v: dvdx=−3⋅3cos(3x)+6⋅(−3sin(3x))=−...
Find the derivative of y=ln|cos(lnx)|. Using Chain Rule to Differentiate Complex FunctionsThe question presents a function that is a composition of three functions, two of which are the natural logarithm function and the third is a cosine function. Using the Chain Rule from Calculus we find...
Use (Figure) to find the slope of the line tangent to the graph of f(x)=x2f(x)=x2 at x=3x=3. Show Solution Finding the Equation of a Tangent Line Find the equation of the line tangent to the graph of f(x)=1/xf(x)=1/x at x=2x=2. Show Solution Find the slope of ...
Find the derivative. y=tan(arcsinx) Derivative of Composite Function: If we have a composition of trigonometric and inverse trigonometric functions (sayT(I(x))), then its derivative is evaluated by applying the chain rule as shown below. ...