How do you find the derivative of #sqrtθ sin θ#?

1 Answer
SagarStudy
Dec 28, 2015

Let #f(x)=sqrt(theta)sintheta##=(theta)^(1/2)sintheta#
differentiate with respect to #theta# using product rule
#(df(x))/(d theta)=(d(theta)^(1/2))/(d theta)sintheta+theta^(1/2)(d(sintheta))/(d theta)#
#implies (df(x))/(d theta)=1/2theta^(1/2-1)sintheta+theta^(1/2)costheta#
#implies (df(x))/(d theta)=1/2theta^(-1/2)sintheta+sqrt(theta)costheta#
#implies (df(x))/(d theta)=1/2(1/theta^(1/2))sintheta+sqrt(theta)costheta#
#implies (df(x))/(d theta)=1/2(1/sqrt(theta))sintheta+sqrtthetacostheta#
#implies (df(x))/(d theta)=1/(2sqrttheta)sintheta+sqrtthetacostheta#

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