Derivatives of Trig Functions
Read this topicExplanations 7
- Now that we know common techniques and limits in trigonometry, the limit definition of a derivative, and how to take the derivative of products and quotients, we can do all sort…
By Leigh Marie Braswell, Moor Xu
- Much like the proof of ddx(sinx)=cosx\frac{d}{dx}(\sin x) = \cos xdxd(sinx)=cosx we will prove that ddx(cosx)=−sinx\frac{d}{dx}(\cos x) = -\sin xdxd(cosx)=−sinx Use the de…
By Joshua Siktar
- Suppose we want to find the derivative of sinx\sin xsinx. There are two approaches- I will explain the one that most people overlook. Remember that a derivative evaluated at x=…
By Vincent Huang
- (Video) Complicated Derivative Examples by PatrickJMT Here's a video by patrickJMT going over some derivative problems that have a mix of different rules. The first problem he l…
By Alex Federspiel
- (Video) Solving Every Derivative Ever by PatrickJMT Okay, maybe it's not EVERY derivative ever but here's a video by patrickJMT going over different derivatives for a whopping 3…
By Alex Federspiel
- (Videos) Derivatives Involving Trigonometric Functions by PatrickJMT Here's a video by patrickJMT showing you how to take derivatives of sine and cosine functions. Luckily, sine…
By Alex Federspiel
- (Video) Deriving Trigonometric Derivative Formulas by PatrickJMT Here's a video by patrickJMT where he shows you how to derive the lesser remembered trig function derivatives us…
By Alex Federspiel
Problems 16
- What's the derivative of (x+3)sinx(x+3) \sin x(x+3)sinx?
- What is the derivative of cosxx\frac{\cos x}{x}xcosx?
- Calculate f′(x)f'(x)f′(x) if f(x)=sin(cos(x))f(x)=\sin(\cos(x))f(x)=sin(cos(x)).
- Calculate f′(x)f'(x)f′(x) if f(x)=esin(x2)f(x)=e^{\sin(x^2)}f(x)=esin(x2).
- Let f(x)=sin2xf(x) = \sin^2 xf(x)=sin2x. Compute f′(π4)f'(\frac\pi4)f′(4π).
- Use differentials to estimate sin(3)\sin(3)sin(3).
- Use differentials to estimate tan(4)\tan(4)tan(4).
- What is the derivative of x4cos(x)x^4\cos(x)x4cos(x)?
- Find the derivative of y=ln(sin2x3)y=\ln(\sin2x^{3})y=ln(sin2x3)
- What is the derivative of sinx\sin xsinx.
- Find the derivative of f(x)f(x)f(x). f(x)=1+cosxx+sinxf(x)=\frac{1+\cos x}{x+\sin x}f(x)=x+sinx1+cosx
- Find the derivative. f(x)=exsinxf(x)=e^{x\sin x}f(x)=exsinx
- Find the second derivative. f(x)=e2xsin(πx)f(x)=e^{2x}\sin(\pi x)f(x)=e2xsin(πx)
- Use linearization to estimate tan(4)\tan(4)tan(4).
- What are the critical points for the function f(x)=ln(cosx)f(x)=\ln(\cos x)f(x)=ln(cosx) on the interval π2<x<3π2\frac{\pi}2<x<\frac{3\pi}22π<x<23π
- Find f'(x) when f(x)=cos3(5x5)f(x)=\cos^3(5x^5)f(x)=cos3(5x5)