Calculate the derivative of cos(x) & understand the proof of the derivation of the derivative of cos(x). Learn the derivatives of the other...
Using the above given trigonometric formulas, we can write the derivative of cos x and the derivative of 1/sec x, that is, d(cos x)/dx = d(1/sec x)/dx, and apply the quotient rule of differentiation.dcosxdx=d(1secx)dx=(1)′secx−(secx)′1sec2x=0.secx−secxtanxsec2x=−...
= 2 (1/cos2x) (sinx/cosx)= 2 sec2x tanxHence, we have proved that the derivative of sec square is equal to 2 sec2x tanx.Derivative of Sec^2x Using Product RuleThe product rule of differentiation is used to find the derivative of the product of two functions. For a function h(x)...
Proving the Sum & Difference Rules for Derivatives Using the Derivatives of Natural Base e & Logarithms Calculating Derivatives of Constant Functions Finding the Derivative of 2sinxcosx Create an account to start this course today Used by over 30 million students worldwide Create an account Explor...
7. (TaNx) y'=1/ tangent function y= (cosx) ^2 8. (Cotx) y'=-1/ cotangent function y= (SiNx) ^2 9. y= (inverse sine function arcsinx y'=1/ 1-x^2 10.) V arccosine function y= (arccosx) y'=-1/ 1-x^2 11. V arctan function y= (arctanx) y'=1/ (1+x^2) 12...
Derivative of a sinusoidal function Homework Statement What is the derivative of ##f(x)=\frac {2x^2} {cos x}##? Homework EquationsThe Attempt at a Solution ##F(x)=\frac {2x^2} {cos x}## So... ##f(x)=2x^2## and ##f'(x)=4x## ##g(x)=cosx## and ##g'(x)=-sinx...
An equality about derivative of a polynomial? Why is $$ \left(x^2-1\right)\frac{d}{dx}\left(x^2-1\right)^n = 2nx\left(x^2-1\right)^{n-1} $$? This is in a textbook and says that its proof is left as an exercise. It seems to be a difficult equality. I believe this...
[test] perspective 1. understand some practical background of the derivative concept (such as instantaneous velocity, acceleration, smooth curve tangent slope etc.); master the definition and derivative derivative function on a point; understanding the concept of derivative function. Memorize 2. basic...
Homework Statement If f(x) = x^5*cos(x^6) find f40(0) and f41(0) The Attempt at a Solution So we are supposed to get the Taylor series and use that to get the value of the derivatives I just manipulated the Taylor series for cosx to get the one for this. Would the value be...
DerivativeProof Replies: 1 Forum:Calculus What Is the Correct Partial Derivative of 6xyz? Homework Statement Find (∂z/∂x) of 6xyz Homework Equations N/a The Attempt at a Solution The correct answer is 6xy(∂z/∂x) but I would like proof of it. I got something different when ...