WebQuestion: 2. Find the derivative of the following functions. f(x) = sin4(x2 + 3x) f(x) = cos4 1 - f(x) = x sin? (2x) f(x) = cos^ [sin(x2)] 3. Determine the intervals in which the following functions are increasing, concave up, and concave down. f(x) = x3 – 3x - 1 f(x) = x6 - 3x4 x2 f(x) = x²+1 h (United States) ... WebJul 13, 2016 · Explanation: In order to differentiate sin3(x), we need to use a chain rule, which tells us that d dx [f (g(x))] = f '(g(x)) ⋅ g'(x) Letting y = sin3(x), then dy dx = 3sin2(x) ⋅ cosx In this problem, we've also performed the power rule, namely by subtracting 1 from the power of 3 on the sinx term, which is why we end up with a sin2(x). Answer link
Derivative With Respect To (WRT) Calculator - Symbolab
WebThe Derivative tells us the slope of a function at any point.. There are rules we can follow to find many derivatives.. For example: The slope of a constant value (like 3) is always 0; The slope of a line like 2x is 2, or 3x is 3 etc; and so on. Here are useful rules to help you work out the derivatives of many functions (with examples below).Note: the little mark ’ means … WebTranscribed Image Text: (a) Find a function f that has y = 4 – 3x as a tangent line and whose derivative is equal to ƒ' (x) = x² + 4x + 1. (b) Find the area under the curve for f (x) = x³ on [−1, 1]. e2t - 2 (c) Determine where the function is f (x) = cos (t²-1) + 3 (d) Express ² sin (x²) dx as limits of Riemann sums, using the right ... coombabah sewage treatment plant
3.5: Derivatives of Trigonometric Functions - Mathematics …
WebThus, sin (kx) is NOT sine times kx. sin (kx) = 1/2 {ie^(-kxi)- ie^(kxi)} Instead, you treat sin(5x-3y) as a single entity. You can break that up using a trigonometric identity, but that is not a more simple form. ... The problem is that you had dy/dx on both sides of the equation, and the goal was to find the derivative of y with respect to x ... WebSep 7, 2024 · Find the first four derivatives of y = sinx. Solution Each step in the chain is straightforward: y = sinx dy dx = cosx d2y dx2 = − sinx d3y dx3 = − cosx d4y dx4 = sinx … WebNov 13, 2024 · From above, we found that the first derivative of sin^3x = 3sin 2 (x)cos(x). So to find the second derivative of sin^2x, we just need to differentiate 3sin 2 (x)cos(x). … family trening