Answer to: Prove that the derivative of sin(x) is cos(x). By signing up, you'll get thousands of step-by-step solutions to your homework questions...
THE 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) − sin x = ...
Answer to: Find the derivative of the function f (x) = sin x cos x. By signing up, you'll get thousands of step-by-step solutions to your homework...
Derivative f’ of the function f(x)=sinx is: f’(x) = cos x for any value of x. Derivative of sin x Derivative $f’$ of the function $f(x)=\sin x$ is: \(\forall x \in ]-\infty, +\infty[ , f'(x) = \cos x\) Proof/Demonstration \[\begin{aligned} \frac{\sin (x+...
Find the derivative ofsin(x+a)cosx View Solution Find the derivative of the function cosxsinx+cosx View Solution Exams IIT JEE NEET UP Board Bihar Board CBSE Free Textbook Solutions KC Sinha Solutions for Maths Cengage Solutions for Maths ...
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...
ddx(sinxcosx)=sinx(−sinx)+cosx(cosx)=−sin2x+cos2x Step 3: Differentiate the right-hand sideNext, we differentiate the right-hand side:ddx(x+y)=ddx(x)+ddx(y)=1+dydx Step 4: Set the derivatives equal to each otherNow we equate the derivatives from both sides:−sin2x+cos2x=...
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: ...
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...
Finally, multiply the derivative of the exponent by the original function, e^(sin x * ln(sin x)). Is there a simpler way to express the derivative of (sin x)^sin x? Yes, you can use the power rule to simplify the derivative of (sin x)^sin x to cos x * (sin x)^sin x *...