A。解析:对于函数\(y = uv\)(这里\(u = x^{2}\),\(v=\sin x\)),根据乘积法则\((uv)^\prime = u^\prime v+uv^\prime\)。\(u = x^{2}\)的导数\(u^\prime = 2x\),\(v=\sin x\)的导数\(v^\prime=\cos x\),所以\(y^\prime = 2x\sin x+x^{2}\cos x\)。选项B中符...
However, there is a simple rule to follow to solve these kinds of problems and that is using the Chain rule. Mathematically, if h(x)=f(x)∘g(x)=f(g(x))thenh′(x)=f′(g(x))⋅g′(x) This means we first take the derivative of the outer function f(x) and treat g(x) ...
We may use common trigonometric derivatives to compute derivative of any function including trigonometric functions. Such as, in the given problem, we've used d dx(sin(x))=cos(x).Answer and Explanation: We are given: y=sinx2 Differentiating both sides, we'll get: {eq}\...
Find the derivative of sin x^(@) w.r.t. x 01:06 Find the derivatives w.r.t. x : sin{f(x)} 01:06 Find the derivatives w.r.t. x : sin(cos x^(2)) 02:41 Find the derivatives w.r.t. x : sin x^(@) 01:46 Find the derivatives w.r.t. x : sin^(-1)(e^(x^(2...
Find the derivative off(x)=sin(7xx+7) Sine and Chain Rule: To calculate the derivative of complex expressions of functions it is necessary to apply the chain rule. This rule, linked to the sine function, results: (sin(g(x)))′=cos(g(x))⋅g′(x). ...
View Solution Find the derivative of cos (x + y) = y with respect to x . View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium NCERT Solutions for Class 11 English Medium NCERT Solutions for Class 10 English Medium ...
Derivative f’ of the function f(x)=sinx is: f’(x) = cos x for any value of x.Derivative of sin xDerivative f′ of the function f(x)=sinx is: ∀x∈]−∞,+∞[,f′(x)=cosxProof/Demonstrationsin(x+h)−sinxh=sin(x)cos(h)+cos(x)sin(h...
f′(x)=11−cos2x⋅−sinx=−sinxsin2x=−sinx|sinx|=−|sinx|sinx. However, as I went to confirm my answer with my instructor, they claimed that my answer was incorrect. Instead, they claimed my work should have gone like so: ...
The derivative of sec xThe derivative of csc xTHE DERIVATIVE of sin x is cos x. To prove that, we will use the following identity:sin A − sin B = 2 cos ½(A + B) sin ½(A − B).(Topic 20 of Trigonometry.)Problem 1. Use that identity to show:sin (x + h) − ...
Differentiation of compound functions can be found by Consider a compound function y=f(g(x)) then its derivative is given by ddxy=ddxf(g(x)) is given by dydx=f′(g(x))g′(x) Some useful derivatives are ddxsinx=cosx